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SQA National 5 Maths Decimals, fractions and percentages

Decimals, fractions and percentages

This page covers the following topics:

Decimal numbers are used to represent a part of a whole number. The decimal point separates the whole number part of a number from its complementary value that is smaller than one. These values that are smaller than one can be interchangeably represented with fractions, decimals, or percentages.

Decimals

Fractions are a way to represent parts of a whole number or mixed numbers. They are denoted by using a numerator and denominator. To add or subtract fractions, the denominators of the fractions must be made the same by multiplying the numerator and denominator by the same number to create equivalent fractions like, for instance, Β²/β‚ˆ and ΒΉ/β‚„. To multiply fractions, find the product of their numerators and of their denominators. And to divide fractions, multiply a fraction with the inverse of the dividing fraction.

Fractions

A percentage is denoted by the β€˜%’ symbol and refers to a part of a whole number in terms of parts per hundred. 17%, for example, means 17 parts out of every 100. A percentage can, therefore, be used to standardise quantities such as, for instance, 20 pencils out of a 200-pencil set which refer to 10% of the set.

Percentages

A percentage is denoted by the β€˜%’ symbol and refers to a part of a whole number in terms of parts per hundred. 17%, for example, means 17 parts out of every 100. If a percentage of a quantity is known, then the original quantity can be calculated with the use of the formula:

Reverse percentages

Appreciation occurs when the value of a good increases and depreciation occurs when the value of a good decreases. Appreciation and depreciation are usually quoted in percentages of an original amount and are given as an annual rate of change such as, for example, a 4% depreciation in the value of a car with every year. Appreciation and depreciation may also compound over a length of time which means that when interest is paid on an amount, the added amount then also receives interest from then on.

Appreciation and depreciation

Fraction, decimals, and percentages are interchangeable ways to represent parts of a whole number and each of the three can either be a positive value or a negative value. These quantities can, therefore, be compared and ordered by using the symbols provided.

Ordering

1

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Express ΒΉΒ²/₇ as a mixed number.

SQA National 5 Maths Decimals, fractions and percentages Express ΒΉΒ²/₇ as a mixed number.
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2

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Simplify 7 + ⁷/β‚„ and express your answer as a mixed number.

SQA National 5 Maths Decimals, fractions and percentages Simplify 7 + ⁷/β‚„ and express your answer as a mixed number.
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3

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What does the β€˜%’ symbol mean?

SQA National 5 Maths Decimals, fractions and percentages What does the β€˜%’ symbol mean?
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4

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Convert 0.172 into a percentage.

SQA National 5 Maths Decimals, fractions and percentages Convert 0.172 into a percentage.
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5

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Todd has 16 glass cups at home. He accidentally breaks 4 when opening and closing his kitchen cabinet. Find how many glasses Todd has broken as a percentage of the total number of glasses he once had.

SQA National 5 Maths Decimals, fractions and percentages Todd has 16 glass cups at home. He accidentally breaks 4 when opening and closing his kitchen cabinet. Find how many glasses Todd has broken as a percentage of the total number of glasses he once had.
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6

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Β£23 represents 65% of what a retail shop worker earns per shift while working part time. Determine what a retail worker usually earns per shift while working part time. Report the answer to two decimal places.

SQA National 5 Maths Decimals, fractions and percentages Β£23 represents 65% of what a retail shop worker earns per shift while working part time. Determine what a retail worker usually earns per shift while working part time. Report the answer to two decimal places.
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7

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May has payed her utility bills but has forgotten to ask for the receipt. She goes to her bank and they tell her that she has 85% of the original amount of money she had in her account at the beginning of the month. Given May has Β£300 left in her account and the only thing she has payed for so far during the month is her utility bill, how much did she originally have? Provide your answer to the nearest whole number.

SQA National 5 Maths Decimals, fractions and percentages May has payed her utility bills but has forgotten to ask for the receipt. She goes to her bank and they tell her that she has 85% of the original amount of money she had in her account at the beginning of the month. Given May has Β£300 left in her account and the only thing she has payed for so far during the month is her utility bill, how much did she originally have? Provide your answer to the nearest whole number.
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8

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One third of a carton of eggs is left for cooking. Given 5 eggs are left, find the initial number of eggs in the carton.

SQA National 5 Maths Decimals, fractions and percentages One third of a carton of eggs is left for cooking. Given 5 eggs are left, find the initial number of eggs in the carton.
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9

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Mary is trying to sell a blouse through an online marketplace. She initially bought it for Β£7 but finds that she can only sell it for Β£3.5. How much has the blouse depreciated in value? Give your answer as a percentage.

SQA National 5 Maths Decimals, fractions and percentages Mary is trying to sell a blouse through an online marketplace. She initially bought it for Β£7 but finds that she can only sell it for Β£3.5. How much has the blouse depreciated in value? Give your answer as a percentage.
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10

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A brand new car initially valued at Β£20000 leaves a car dealership. The salesman estimates that the car will depreciate at an annual compound rate of 4%. If the car is used for 5 years before it is resold to another owner, find the value at which the car will be sold to two decimal places.

SQA National 5 Maths Decimals, fractions and percentages A brand new car initially valued at Β£20000 leaves a car dealership. The salesman estimates that the car will depreciate at an annual compound rate of 4%. If the car is used for 5 years before it is resold to another owner, find the value at which the car will be sold to two decimal places.
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