Ostukorv on tühi
DOING MULTIPLICATION ON PAPER
Tim bought 3 sheets of wrapping paper. How much did he pay if 1 sheet cost 132 euro?
1 sheet 3 sheets
132 euro
132 euro 132 euro 132 euro
? euro
132 euro + 132 euro + 132 euro =
euro
Estimate:
132 + 132 + 132 \latex{ \approx } 130 + 130 + 130 = 390.
Calculation:
The sum is 396. This tallies with the estimate.
= 396.
Tim paid 396 Ft for 3 sheets of wrapping paper.
132
132
+132
396
The same result can be obtained by multiplication:
132 euro \latex{ \times } 3 =
euro
Estimate:
132 \latex{ \times } 3 \latex{ \approx } 130 \latex{ \times } 3 = 390.
Doing multiplication on paper starts with the digits in the units' place, therefore the multiplier is written next to the units.
hundreds
tens
units
1
3
2
\latex{ \times } 3
3
9
6
1
3
2
·3
3
9
6
multiplicand
multiplier
product
• 3 times 2 units equal 6 units.
• 3 times 3 tens equal 9 tens.
• 3 times 1 hundred equals 3 hundreds.
The product is 396. This tallies with the estimate.
= 396.
Check:
132
132
+132
396
? euro
The price of 3 sheets is 396 euro; that is how much Tim paid.
{{exercise_number}}. Calculate the products. Estimate first with values rounded to the nearest tens, and check the results afterwards by addition on paper.
Est:
Est:
Est:
Est:
Est:
112·3
134·2
213·3
412·2
121·4
Check:
112
112
+112
{{exercise_number}}. One bar of chocolate costs 213 euro. Maggie bought one bar each for her two siblings and herself. How much did she pay? Mark the correct solutions with a *. Calculate.
213 + 213 \latex{ \times } 2 =
213 \latex{ \times } 3 =
213 + 213 \latex{ \times } 3 =
213 + 213 =
213 + 213 + 213 =
213 \latex{ \times } 2 =
{{exercise_number}}. Form three-digit numbers with the digits 3, 2 and 1 without using the same digit twice. Calculate the product of these numbers when multiplied by 2 and 3.
{{exercise_number}}. Calculate the products, then colour the numbered squares according to the results.
341 \latex{ \times } 2
132 \latex{ \times } 3
204 \latex{ \times } 2
310 \latex{ \times } 3
112 \latex{ \times } 4
6
8
2
1
1
0
4
4
8
1
4
0
8
9
9
2
7
2
3
9
6
0
9
3
0
4
5
{{exercise_number}}. Solve the word problems.
- 2nd, 3rd and 4th form pupils took part in the county maths competition, 122 pupils from each form. How many pupils in total competed?
one form
122
122 122 122
122·3=
number of forms
3
?
total
?
122·3
366
=366
Check:
122
122
+122
366
Est.:
360
In total pupils took part in the competition.
366
- Chris lives 324 metres from the school, and Robert lives twice as far. How far is Robert's home from the school?
- If 1 m of fabric costs 442 euro, how much does 2 m cost?
- I thought of a number. Twice this number is 212. How much is 6 times this number?
{{exercise_number}}. Write the factors in the correct squares. Keep trying.
2
331
4
202
413
102
3
2
· =826
· =993
· =204
· =808
{{exercise_number}}. Which numbers satisfy the inequalities?
441 \latex{ \times } 2 >
:
312 \latex{ \times } 3 <
\latex{ \times } 10
:
\latex{ \times } 100 > 112 \latex{ \times } 4
:
{{exercise_number}}. Which is greater? Fill in the correct relational signs without doing the multiplication.
a) 114 \latex{ \times } 2
214 \latex{ \times } 2
312 \latex{ \times } 3
321 \latex{ \times } 3
121 \latex{ \times } 4
101 \latex{ \times } 4
b) 102 \latex{ \times } 3
202 \latex{ \times } 3
131 \latex{ \times } 3
133 \latex{ \times } 3
142 \latex{ \times } 2
142 \latex{ \times } 1
c) 201 \latex{ \times } 3
102 \latex{ \times } 3
332 \latex{ \times } 2
221 \latex{ \times } 2
111 \latex{ \times } 2
222 \latex{ \times } 1
{{exercise_number}}. What is the product?
One factor is 413, the other is 2:
The factors are 221 and 4:
The multiplier is 3, the multiplicand is
231:
•
•
•
Mum used a 124 cm ribbon to fringe a cushion. What length of ribbon does she need to do 4 cushions?
1 cushion 4 cushions
124 cm
? cm
124 cm 124 cm 124 cm 124 cm
? cm
124 cm \latex{ \times } 4 =
cm
Estimate:
124 \latex{ \times } 4 \latex{ \approx } 120 \latex{ \times } 4 = 480.
h
t
u
1
2
4
\latex{ \times } 4
4
4
8
9
1
6
6
+1
1
2
4
·4
4
9
6
• four times 4 units are equal to 16 units.
Write down the 6 units, and add the 1 ten to the tens multiplied.
• four times 2 tens are equal to 8 tens, plus 1 ten is 9 tens.
• four times 1 hundred equals 4 hundreds.
The product is 496. This tallies with the estimate.
= 496.
Mum needs a 496 cm long ribbon to fringe 4 cushions.
Check:
124
124
124
+124
496
{{exercise_number}}. Calculate the product. Estimate first with values rounded to the nearest tens, and check the results by addition on paper.
Est:
Est:
Est:
Est:
Est:
247·2
328·3
114·4
205·4
226·2
Check:
247
+247
{{exercise_number}}.
a)
127 kg of bananas and twice as much of apples were delivered to the shop.
How many kilograms of apples were delivered?
How many kilograms of apples were delivered?
b)
How many kg of fruits in total were delivered?
c)
Mick bought 3 kg of the 116 euro apples, while Charlie bought 2 kg of the 318 euro bananas. Which of them paid more?
{{exercise_number}}. Arrange the products in decreasing order by estimating. Check the order after doing the calculations.
Est:
246 \latex{ \times } 2
128 \latex{ \times } 3
346 \latex{ \times } 2
426 \latex{ \times } 2
107 \latex{ \times } 4
218 \latex{ \times } 3
{{exercise_number}}. The arrows point at the greater number. Write the products in the drawings.
115 \latex{ \times } 5
218 \latex{ \times } 3
209 \latex{ \times } 4
317 \latex{ \times } 3
147 \latex{ \times } 2
{{exercise_number}}.
- One rose costs 126 euro. Nelly bought 3 for her mother. How much did she pay?
- The weight of a packet of wafers is 115 grams. Grandad bought two packets of lemon-filled and two packets of chocolate wafers. What is the total weight of the wafers?
- Last summer 216 children went to the school holiday camp. This year the camp can accomodate three times as many pupils. At most how many children can go to the camp this summer?
{{exercise_number}}. Fill in the tables. Estimate with values rounded to the nearest tens.
multiplicand
multiplier
estimated
product
product
multiplicand
multiplier
estimated
product
product
126
3
215
4
317
2
224
3
219
3
435
2
106
6
117
5
{{exercise_number}}. Which numbers satisfy the inequalities?
248 \latex{ \times } 2 >
:
127 \latex{ \times } 3 <
< 216 \latex{ \times } 4
:
308 \latex{ \times } 3 >
+ 100
:
{{exercise_number}}. Form three-digit numbers using the digits 4, 0 and 3 without using digits twice.
(In the three-digit numbers there may be no '0' in the hundreds' place). Multiply the numbers by 2.
{{exercise_number}}.
- I thought of a number, added the same number, and multiplied the sum by 2. The result is how many times the number I thought of?
- I multiplied 127 by 2 and added the result to 127. What number did I obtain?
- I thought of a number, multiplied it by ten, then wrote at the end the original number multiplied by 2, and the number I got was 204. Which number did I think of?
A school ordered 172 benches and twice as many chairs. How many chairs were ordered?
school benches
chairs
172 pcs
< ? pcs
\latex{ \times } 2
172 pcs
172 db \latex{ \times } 2 =
pcs
Estimate:
172 \latex{ \times } 2 \latex{ \approx } 170 \latex{ \times } 2 = 340.
h
t
u
1
7
2
\latex{ \times } 2
2
3
1
4
4
4
4
+1
• 2 times 2 units equal 4 units.
• 2 times 7 tens equal 14 tens.
Write down the 4 tens, and add the 1 hundred to the hundreds multiplied.
Write down the 4 tens, and add the 1 hundred to the hundreds multiplied.
• 2 times 1 hundred equals 2 hundreds, plus 1 hundred equals 3 hundreds.
1
7
2
·2
3
4
4
The product is 344. This tallies with the estimate.
= 344. The school ordered 344 chairs.
Check:
172
+172
344
{{exercise_number}}. Calculate the product. Estimate first with values rounded to the nearest tens, and check afterwards with multiplication on paper.
Est:
Est:
Est:
Est:
Est:
263·3
181·5
454·2
91·6
172·4
Check:
263
263
+263
{{exercise_number}}. Connect the corresponding amounts. Calculate the product exactly.
281 \latex{ \times } 2
142 \latex{ \times } 4
209 \latex{ \times } 3
162 \latex{ \times } 4
\latex{ \approx } 210 \latex{ \times } 3
\latex{ \approx } 280 \latex{ \times } 2
\latex{ \approx } 160 \latex{ \times } 4
\latex{ \approx } 140 \latex{ \times } 4
{{exercise_number}}. I thought of an odd number greater than 169, but smaller than 172. I multiplied it by 4. What is the result?
{{exercise_number}}.
- 132 doors were installed in one of the buildings of a housing estate under construction. How many doors will be needed in 4 similar houses?
- Sue wants to take home 4 slices of the same cake for her family. One slice of chocolate cake costs 142 euro, the fruit cake costs 117 euro. Which cake will she buy if she has 500 euro?
- How long a film can be recorded on 3 video tapes of 240 minutes recording each time?
{{exercise_number}}. Continue filling in the chart according to the rule.
241
73
84
263
172
141
92
131
4
2
2
3
4
5
3
6
964
146
=
\latex{ \times }
{{exercise_number}}.
- Which numbers did I think of?
- Four times 152.
- The product of multiplying 8 by 61.
- 178 multiplied by five.
- Write multiplication describing the scale drawings.
153
153
153
263
263
281
281
281
?
?
?
{{exercise_number}}. Which numbers justify the calculations?
253 \latex{ \times } 3 >
162 \latex{ \times } 4 <
81 \latex{ \times } 6 <
+ 100
:
:
:
{{exercise_number}}.
a)
64 visitors saw the exhibition on Saturday morning, and twice as many in the afternoon. How many people in total visited the exhibiton on Saturday?
b)
On the other days of the week four times as many visitors came to see the exhibiton as on Saturday. How many people visited the exhibiton during the week?
{{exercise_number}}.
- I multiplied 132 by a number, and the product I obtained was 396. Which number is the multiplier?
Write down with a mathematical sentence.
132 \latex{ \times }
= 396.
This sentence can be answered with an incomplete multiplication.
Check:
132
132
+132
396
132·
396
3 times
3 times
3 times
2 units = 6 units.
3 tens = 9 tens.
1 hundreds = 3 hundreds.
132·
396
3
= 3
- Write the multiplier in the square marked. Keep trying.
234·
468
122·
366
406·
812
127·
381
113·
565
147 tree seedlings were planted in a forest every day. How many seedlings were planted in 3 days?
1 day
3 days
147 pcs
? pcs
147 pcs
147 pcs
147 pcs
? pcs
147 pcs \latex{ \times } 3 =
pcs
Estimate:
147 \latex{ \times } 3 \latex{ \approx } 150 \latex{ \times } 3 = 450.
h
t
u
1
4
7
\latex{ \times } 3
3
1
2
2
1
4
4
1
+1
+2
1
4
7
4
4
1
·3
• 3 times 7 units equal 21 units. Write down the 1 unit, add the 2 tens to the tens multiplied
• 3 times 4 tens equal 12 tens, plus 2 tens equal 14 tens. Write down the 4 tens, add the one hundred to the hundreds multiplied.
• 3 times 1 hundred equals 3 hundreds, plus 1 hundred equals 4 hundreds.
The product is 441.
It tallies with the estimate.
= 441.
In 3 days 441 tree seedlings were planted.
Check:
147
147
+147
441
{{exercise_number}}. Calculate the product. First estimate with values rounded to the nearest tens, and check afterwards with multiplication on paper.
Est:
Est:
Est:
Est:
Est:
Check:
247·3
183·4
196·5
84·6
369·2
247
247
+247
{{exercise_number}}. How many three-digit numbers can you form uing the digits 4, 5, 2?
• What is four times the smallest three-digit number?
• What is three times the smallest three-digit even number?
• What is two times the greatest three-digit number?
·4
·3
·2
{{exercise_number}}.
Kate was 86 cm tall when she was 3 years old. Now she is twice as tall. What is her height today?
{{exercise_number}}.
Claire bought 3 cactus pots. How much did she pay if one cactus pot costs 245 euro?
There are 179 seats in the balcony of a cinema, and three times as many on the ground floor. How many people in total can be seated in the cinema?
Maggie has read 76 pages of a book. How many pages does it contain, if she has reached one third of the book?
a)
b)
c)
{{exercise_number}}.
- Multiply the following numbers by four.
Decide if the statements are true or false for the products you obtained above.
Write the letter T or F in the squares.
Every product is an even number.
There are products greater than 700.
246 multiplied by 4 is greater than four times 198.
The product of even numbers is also an even number.
{{exercise_number}}.
a)
A number multiplied by 2 is 186. What is this number multiplied by four?
b)
2 kg of apples costs 156 euro. What is the price of 6 kg?
c)
Mary bought 3 identical notebooks for a total of 156 euro.
How much would 9 similar notebooks cost?
How much would 9 similar notebooks cost?
\latex{ \times } 2 =
186
\latex{ \times }
\latex{ \times }
\latex{ \times } 4 =
{{exercise_number}}. One box contains 86 chocolates. Fill in the chart.
number of boxes
number of chocolates
1
2
6
9
3
8
4
86
{{exercise_number}}. Which numbers justify the inequalities?
234 \latex{ \times } 4 >
167 \latex{ \times } 3 <
\latex{ \times } 10
145 \latex{ \times } 6 >
> 79 \latex{ \times } 8
:
:
:
{{exercise_number}}.
- Circle those numbers which, if multiplied by 3, give an even number.
274, 413, 379, 453, 178, 155
- Check by doing the multiplication on paper.
{{exercise_number}}.
Fred gave his phone number describing it like this: the first three digits is twice 76. The next three digits is three times the first three digits. What is Fred's phone number?
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