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ESO Y1 · Mathematics
Numbers · Decimal numbers

Operations with decimal numbers

You pay with a $50$ € note and buy a phone case for $12{,}45$ € and a screen protector for $8{,}90$ €. How much change do you get? Decimals are handled almost exactly like whole numbers, with one extra thing to watch: lining up the decimal point.

Adding and subtracting decimals

Vertical addition of $12{,}45$ and $8{,}90$ highlighting the vertical alignment of the decimal points to obtain $21{,}35$. 12,45 + 8,90 21,35 decimal points aligned in the same column
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In a mobile phone accessory shop, Marc wants to buy a case costing $12,45$ € and a screen protector costing $8,90$ €. If Marc pays with a $50$ € note, how much change…

In a mobile phone accessory shop, Marc wants to buy a case costing $12,45$ € and a screen protector costing $8,90$ €. If Marc pays with a $50$ € note, how much change will he receive at the till?

Solve
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Copy and complete the following statements by writing the missing decimal number to make each calculation correct: a) $15,45 + \dots = 20$ b) $7,2 - \dots = 4,55$ c)…

Copy and complete the following statements by writing the missing decimal number to make each calculation correct:

  1. a) $15,45 + \dots = 20$
  2. b) $7,2 - \dots = 4,55$
  3. c) $\dots \cdot 3 = 12,9$
Solve
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Three friends decide to have an afternoon snack together. They buy a pack of soft drinks for $4,85$ €, a family-size bag of crisps for $2,30$ € and a box of small cakes…

Three friends decide to have an afternoon snack together. They buy a pack of soft drinks for $4,85$ €, a family-size bag of crisps for $2,30$ € and a box of small cakes for $5,45$ €. If they pay with a $20$ € note, how much money will they have left over to buy sweets afterwards?

Solve

Multiplying decimals

Diagram of decimal multiplication showing the count of the factors' decimal places to position the decimal point in the result. 2,5 · 1,80 1 place + 2 places = 3 decimal places = 4,500
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Work out these calculations mentally using powers of ten. Remember to move the decimal point to the correct side depending on whether you multiply or divide: a)…

Work out these calculations mentally using powers of ten. Remember to move the decimal point to the correct side depending on whether you multiply or divide:

  1. a) $34,57 \cdot 10$
  2. b) $0,23 \cdot 100$
  3. c) $458,2 : 10$
  4. d) $12,5 : 1000$
Solve
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Marta went to the greengrocer's and bought $2,5$ kg of apples at $1,80$ € per kilogram. On arriving home, she notices that one of the apples is bad and decides to return…

Marta went to the greengrocer's and bought $2,5$ kg of apples at $1,80$ € per kilogram. On arriving home, she notices that one of the apples is bad and decides to return it. If the apple weighed $0,25$ kg, how much money should Marta be refunded?

1,80 €/kg Total bought 2,5 kg Returned apple 0,25 kg Refund ? €
Solve
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In a "Back to School" offer, a pack of $5$ notebooks costs $8,25$ €, whereas if you buy them individually, each one costs $1,80$ €. What is the total saving if we decide…

In a "Back to School" offer, a pack of $5$ notebooks costs $8,25$ €, whereas if you buy them individually, each one costs $1,80$ €.

What is the total saving if we decide to buy $15$ notebooks using the pack offer instead of buying them separately?

Solve

Dividing decimals

Transformation of the division $4{,}8 : 1{,}2$ into $48 : 12 = 4$ by multiplying both terms by $10$. 4,8 : 1,2 ×10 both(decimal points removed) 48 : 12 = 4
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To make a recipe, we need to divide a $1,5$ kg bag of flour into $6$ equal portions to make muffins. How many kilograms of flour will each portion weigh? Express your…

To make a recipe, we need to divide a $1,5$ kg bag of flour into $6$ equal portions to make muffins. How many kilograms of flour will each portion weigh? Express your answer in grams as well.

Solve
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A spool of filament for a 3D printer weighs exactly $1,25$ kg. If $0,015$ kg of plastic is used to make a small part, how many complete parts can be made from a single…

A spool of filament for a 3D printer weighs exactly $1,25$ kg. If $0,015$ kg of plastic is used to make a small part, how many complete parts can be made from a single spool? How much filament will be left over at the end?

1,25 kg Complete spool make parts 0,015 kg 1 part Total = 1,25 kg 1 2 3 ... n 0,015 n = ? r
Solve

Combined operations and money problems

Problems with decimals often mix several operations: the important thing is to write the whole expression before calculating.

Diagram of a rectangular park $25{,}4$ m long by $12{,}75$ m wide for calculating the perimeter and the total cost of the fencing. perimeter: 2·(25,4+12,75) = 76,3 m 76,3 · 15,20 = 1.159,76 €budget is enough
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Work out the following combined operations, respecting the order of operations (brackets, multiplications/divisions, and finally additions/subtractions): a)…

Work out the following combined operations, respecting the order of operations (brackets, multiplications/divisions, and finally additions/subtractions):

  1. a) $4,5 + 2,1 \cdot 3$
  2. b) $(12,8 - 3,4) : 2$
  3. c) $5 \cdot 0,25 + 1,75$
Solve
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A group of $4$ friends goes to the cinema. The total for tickets and popcorn came to $45,80$ €. If they decide to split the cost equally, how much money must each person…

A group of $4$ friends goes to the cinema. The total for tickets and popcorn came to $45,80$ €. If they decide to split the cost equally, how much money must each person pay? If one of them only has a $10$ € note and a $2$ € coin, will they have enough money?

Total: 45,80 € Divided into 4 equal parts ? + ? + ? + ? 10€ + 2€ Available: 12,00 €
Solve
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Calculate the result of the following combined operations, respecting the order of operations: a) $12,5 + 3,8 \cdot (6,4 - 2,15)$ b) $(15,4 + 8,6) : 2,5 - 1,02 \cdot 4$

Calculate the result of the following combined operations, respecting the order of operations:

  1. a) $12,5 + 3,8 \cdot (6,4 - 2,15)$
  1. b) $(15,4 + 8,6) : 2,5 - 1,02 \cdot 4$
Solve

Summary

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