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Adding and subtracting decimal numbers
Example 1
A group of cyclists covered \latex{ 71.4 } \latex{ km } on the first day, \latex{ 59.1 } \latex{ km } on the second, and
\latex{ 65.3 } \latex{ km } on the third day. How many \latex{ kilometres } did they cover in total?
Solution
I. Convert the distances into \latex{ metres } and add them:
II. Write the numbers below each other according to the place values and add them:
Day \latex{ 1 }:
Day \latex{ 2 }:
Day \latex{ 3 }:
Total:
\latex{+}
\latex{+}
\latex{ m }
\latex{ m }
\latex{ m }
\latex{ m }
\latex{ km }
\latex{ km }
\latex{ km }
\latex{ km }
\latex{ . }
\latex{ . }
\latex{ . }
\latex{ . }
\latex{ = }
\latex{ = }
\latex{ = }
\latex{ = }
\latex{ 7 }
\latex{ 1 }
\latex{ 4 }
\latex{0 }
\latex{0 }
\latex{ 5 }
\latex{ 9 }
\latex{ 1 }
\latex{ 0 }
\latex{ 0 }
\latex{ 6 }
\latex{ 5 }
\latex{ 3 }
\latex{ 0 }
\latex{ 0 }
\latex{ 1 }
\latex{ 9 }
\latex{ 5 }
\latex{ 8 }
\latex{ 0 }
\latex{ 0 }
\latex{ , }
\latex{ 7 }
\latex{ 1 }
\latex{ 4 }
\latex{ 1 }
\latex{ 3 }
\latex{ 8 }
\latex{ 9 }
\latex{ 5 }
\latex{ 5 }
\latex{ 5 }
\latex{ 6 }
\latex{ 9 }
\latex{ 1 }
You get the same result in both cases: the cyclists covered a total distance of
\latex{ 195.8 } \latex{ km }.
Example 2
In a store, \latex{ 1.35 } \latex{ m } of a \latex{ 15.4 } \latex{ m } long fabric was sold. How much fabric was left?
Solution
I. Convert the length of the fabrics into \latex{ centimetres } and perform subtraction:
II. Write them below each other as if they were natural numbers:
initial:
sold:
left:
\latex{-}
\latex{-}
\latex{ cm }
\latex{ cm }
\latex{ cm }
\latex{ m }
\latex{ m }
\latex{ m }
\latex{ . }
\latex{ . }
\latex{ . }
\latex{ = }
\latex{ = }
\latex{ = }
\latex{ 1 } \latex{ , }
\latex{ 5 }
\latex{4 }
\latex{0 }
\latex{5 }
\latex{3 }
\latex{1 }
\latex{ 1 }
\latex{ 4 }
\latex{ 0 }
\latex{ 5 }
\latex{ , }
\latex{ 5 }
\latex{ 1 }
\latex{ 4 }
\latex{ 0 }
\latex{ 5 }
\latex{ 3 }
\latex{ 1 }
\latex{ 4 }
\latex{ 1 }
\latex{ 0 }
\latex{ 5 }
In both cases, you get the same result: \latex{ 14.05 } \latex{ m } of fabric was left.
When adding or subtracting decimal numbers, write the digits with the same place value below each other. This way, the decimal points will also be under each other. After performing the operation, write the decimal point in the sum or difference at the appropriate place.
Exercises
{{exercise_number}}. Perform the additions in your head.
a) \latex{2+0.3}
b) \latex{12 + 0.8}
c) \latex{5 + 0.12}
d) \latex{23 + 0.07}
e) \latex{10 + 0.452}
f) \latex{83 + 0.017}
g) \latex{34 + 0.06}
h) \latex{0.2 + 8}
i) \latex{0.55 + 15}
j) \latex{0.012 + 9}
k) \latex{37 + 0.053}
l) \latex{152 + 0.152}
{{exercise_number}}. Perform the additions.
a) \latex{2.3 + 0.9}
b) \latex{3.5 + 1.9}
c) \latex{18.8 + 7.2}
d) \latex{13.35 + 1.25}
e) \latex{178.4 + 2.7}
f) \latex{93.47 + 16.53}
g) \latex{0.3 + 0.05}
h) \latex{1.4 + 0.12}
i) \latex{8.12 + 0.045}
j) \latex{12.4 + 3.45}
k) \latex{42.6 + 1.25}
l) \latex{11.345 + 8.655}
{{exercise_number}}. A lorry can carry \latex{ 3.25 } \latex{ tonnes }, while its trailer can bear a load of \latex{ 2.8 } \latex{ tonnes }. How many \latex{ tonnes } of cargo can the lorry and its trailer carry in total?
{{exercise_number}}. Which lorry has to turn back if vehicles over \latex{ 6 } \latex{ tonnes } are not allowed on the road?
a)
\latex{ 3.8 } \latex{ t }
\latex{ 1.895 } \latex{ t }
b)
\latex{ 3.6 } \latex{ t }
\latex{ 2.95 } \latex{ t }
c)
\latex{ 4.620 } \latex{ t }
\latex{ 1.728 } \latex{ t }
d)
\latex{ 3.390 } \latex{ t }
\latex{ 2.4 } \latex{ t }
{{exercise_number}}. A sign prohibits lorries over \latex{ 3.8 } \latex{ metres } from entering the tunnel. Which container can be transported through the tunnel if the trailer is \latex{ 1.2 } \latex{ m } high?
a)
\latex{ 2.55 } \latex{ m }
b)
\latex{ 2.06 } \latex{ m }
c)
\latex{ 1.98 } \latex{ m }
d)
\latex{ 2.60 } \latex{ m }
{{exercise_number}}. The table shows the results of the two races of an Alpine ski race. (→)
Who won the race if the winner is the skier with the lowest overall time of the two races?
Calculate the overall time results and determine the final order of the race.
Name
Race I
Race II
Brown, T.
Harrison, T.
Kellerman, F.
Lawson, L.
Scofield, P.
Verrier, S.
\latex{ 53.47 } \latex{ s }
\latex{ 52.34 } \latex{ s }
\latex{ 52.96 } \latex{ s }
\latex{ 51.86 } \latex{ s }
\latex{ 52.41 } \latex{ s }
\latex{ 53.01 } \latex{ s }
\latex{ 52.78 } \latex{ s }
\latex{ 52.17 } \latex{ s }
\latex{ 53.18 } \latex{ s }
\latex{ 52.63 } \latex{ s }
\latex{ 51.97 } \latex{ s }
\latex{ 52.10 } \latex{ s }
{{exercise_number}}. Perform the subtractions in your head.
a) \latex{12.3 - 0.3}
b) \latex{52.8 - 0.8}
c) \latex{34.22 - 0.12}
d) \latex{43.12 - 0.07}
e) \latex{10 - 0.4}
f) \latex{18.2 - 0.17}
g) \latex{34 - 0.06}
h) \latex{10.7 - 0.8}
i) \latex{0.73 - 0.65}
j) \latex{0.082 - 0.01}
k) \latex{72 - 0.01}
l) \latex{23 - 0.12}
{{exercise_number}}. Perform the subtractions.
a) \latex{2.3 - 0.9}
b) \latex{3.5 - 1.9}
c) \latex{18.8 - 7.2}
d) \latex{13.35 - 1.25}
e) \latex{178.4 - 2.7}
f) \latex{93.47 - 16.53}
g) \latex{0.3 - 0.05}
h) \latex{1.4 - 0.12}
i) \latex{8.12 - 0.045}
j) \latex{12.4 - 3.45}
k) \latex{42.6 - 1.25}
l) \latex{11.345 - 8.655}
{{exercise_number}}. How many \latex{ kilograms } of apples are in the basket in the drawing? (→)
{{exercise_number}}. A male stag beetle can measure up to \latex{ 8.5 } \latex{ centimeters } in length, while a European spruce bark beetle can measure up to \latex{ 0.4 } \latex{ centimetres }. How much longer is the male stag beetle than the European spruce bark beetle?
{{exercise_number}}. Gabe records the values on the gas meter every \latex{ month }. During which \latex{ month } did he use the most and the least gas? What is the difference in the gas used during these two \latex{ months? } (→)
\latex{ 1 } November
\latex{ 1 } December
\latex{ 1 } January
\latex{ 1 } February
\latex{ 1 } March
\latex{ 13,418.481 } \latex{ m^{3} }
\latex{ 14,277.895 } \latex{ m^{3} }
\latex{ 15,306.063 } \latex{ m^{3} }
\latex{ 16,126.475 } \latex{ m^{3} }
\latex{ 16,742.673 } \latex{ m^{3} }
{{exercise_number}}. Perform the additions.
a) \latex{1.2 + 2.3 + 3.4 + 4.5 + 5.6}
b) \latex{7.019 + 0.81 + 19.999 + 0.1}
c) \latex{2.82 + 0.27 + 17.9 + 10.63}
d) \latex{5.617 + 438.3 + 0.18 + 3.22}
e) \latex{3.78 + 20.42 + 13.55 + 0.45}
f) \latex{76.333 + 3.7 + 86.4 + 0.987}
{{exercise_number}}. What digits should replace the letters to make the additions true?
a)
b)
c)
d)
{{exercise_number}}. The first concrete mixer truck brought \latex{ 11.6 } \latex{ tonnes } of concrete to the construction site, the second \latex{ 10.7 } \latex{ tonnes }, and the third \latex{ 8.25 } \latex{ tonnes }. How many \latex{ tonnes } of concrete did the three mixer trucks take to the construction site in total?
{{exercise_number}}. Calculate the difference between the sums \latex{ A } and \latex{ B }.
\latex{\text{A} = 613.45 + 108.746 + 12.202 + 1.2002}
\latex{\text{B} = 714.702 + 28.8 + + 1.2345 + 2.8765}
\latex{\text{B} = 714.702 + 28.8 + + 1.2345 + 2.8765}
{{exercise_number}}. You have bought three meat packages weighing \latex{ 1.347 } \latex{ kg }, \latex{ 1.284 } \latex{ kg } and \latex{ 1.436 } \latex{ kg }. How many \latex{ kilograms } of meat have you purchased in total?
{{exercise_number}}. There were \latex{ 23.68 } \latex{ tonnes } of sugar in a warehouse when a \latex{ 12.4 } \latex{ t } shipment arrived. After taking the new shipment to the warehouse, four merchants bought from the sugar. The first bought \latex{ 1.6 } \latex{ tonnes }, the second \latex{ 1,860 } \latex{ kilogram }s, the third \latex{ 0.95 } \latex{ tonnes } and the fourth \latex{ 1.18 } \latex{ tonnes }. How many \latex{ tonnes } of sugar was left in the warehouse?
{{exercise_number}}. A family took €\latex{ 1,500 } for a trip abroad. They spent €\latex{ 487.9 } during the first \latex{ week } and €\latex{ 629.8 } during the second. Can they still buy a camera that costs €\latex{ 380 ?}
{{exercise_number}}.
a) What is the difference if the subtrahend is \latex{ 1.5 } and the minuend is \latex{ 2.45 ?}
b) What is the minuend if the difference is \latex{ 17.435 } and the subtrahend is \latex{ 125.65 ?}
c) What is the subtrahend if the difference is \latex{ 0.1038 } and the minuend is \latex{ 4.8962 ?}
b) What is the minuend if the difference is \latex{ 17.435 } and the subtrahend is \latex{ 125.65 ?}
c) What is the subtrahend if the difference is \latex{ 0.1038 } and the minuend is \latex{ 4.8962 ?}
{{exercise_number}}. The largest freshwater fish in Europe is the wels catfish. The largest recorded specimen was \latex{ 4.57 } \latex{ m } long and weighed \latex{ 336.3 } \latex{ kg }. The smallest freshwater fish is the dwarf pygmy goby, measuring
\latex{ 7.5 } \latex{ mm } in length and weighing \latex{ 0.002 } \latex{ grams }. What is the
a) difference between their lengths;
b) difference between their masses?
{{exercise_number}}. The giant Borneo stick insect is the longest insect in the world, measuring \latex{ 32 } \latex{ cm } in length. The smallest insect is the parasitoid wasp, measuring \latex{ 0.21 } \latex{ mm } in length. How many \latex{ centimetres } is the difference between the length of the longest and the smallest insect?
{{exercise_number}}. The difference between neighbouring numbers on the snakes is equal. What numbers should be written in place of the letters?
a)
b)
c)
d)
\latex{ 0.9 }
\latex{ 1.6 }
\latex{ 2.3 }
\latex{A}
\latex{B}
\latex{C}
\latex{D}
\latex{E}
\latex{F}
\latex{A}
\latex{B}
\latex{C}
\latex{D}
\latex{E}
\latex{F}
\latex{ 13.5 }
\latex{ 14.4 }
\latex{ 15.3 }
\latex{A}
\latex{B}
\latex{C}
\latex{ 21.4 }
\latex{ 23.7 }
\latex{ 26 }
\latex{D}
\latex{E}
\latex{F}
\latex{A}
\latex{B}
\latex{C}
\latex{D}
\latex{ 3.48 }
\latex{ 4.45 }
\latex{ 5.42 }
\latex{E}
\latex{F}
{{exercise_number}}. What numbers can replace the letters in the magic squares so that the sum of the numbers in every row, column and diagonal is the same?
a)
\latex{A}
\latex{B}
\latex{C}
\latex{E}
\latex{D}
\latex{ 0.1 }
\latex{ 0.8 }
\latex{ 0.3 }
\latex{ 0.4 }
b)
\latex{F}
\latex{G}
\latex{H}
\latex{J}
\latex{I}
\latex{ 0.87 }
\latex{ 0.66 }
\latex{ 0.8 }
\latex{ 0.45 }
c)
\latex{K}
\latex{L}
\latex{N}
\latex{O}
\latex{M}
\latex{ 13 }
\latex{ 10 }
\latex{ 7 }
\latex{ 8.5 }
d)
\latex{P}
\latex{Q}
\latex{T}
\latex{S}
\latex{R}
\latex{ 6.2 }
\latex{ 3.2 }
\latex{ 3.8 }
\latex{ 2 }
e)
\latex{A}
\latex{B}
\latex{E}
\latex{C}
\latex{D}
\latex{ 1.4 }
\latex{ 2.1 }
\latex{ 1.6 }
\latex{ 1.7 }
f)
\latex{F}
\latex{G}
\latex{H}
\latex{J}
\latex{I}
\latex{ 8.7 }
\latex{ 6.6 }
\latex{ 8 }
\latex{ 4.5 }
g)
\latex{K}
\latex{L}
\latex{M}
\latex{N}
\latex{O}
\latex{ 1.3 }
\latex{ 1.0 }
\latex{ 0.7 }
\latex{ 0.85 }
h)
\latex{P}
\latex{Q}
\latex{R}
\latex{T}
\latex{S}
\latex{ 0.26 }
\latex{ 0.42 }
\latex{ 0.5 }
\latex{ 0.74 }
Quiz
Make a \latex{ 3\times3 } magic square using numbers greater than \latex{2} but smaller than \latex{3} with exactly one decimal digit.
