Step-by-step Maths Level 5: Fractions, measures, perimeter, time and money
Part of the Step-by-step Maths Level 5 level 5 check chapter. Chapter overview · whole chapter on one page
Fractions, measures, perimeter, time and money
To add fractions with the same denominator, add the top numbers and keep the bottom number. Simplify when you can.
For time and money, count on in steps and keep the units and the decimal points in line.
Key ideas
- Add the top numbers; keep the bottom number.
- Change measures to the same unit first.
- Count on across the hour or midnight.
Method. More than one whole: add the top numbers, then write the whole ones out.
- Add the top numbers. Keep the bottom number the same.3 + 2 = 5
- Write the total. 5 parts of size 1/4.5/4
- Write as a mixed number. There are 1 whole one and 1/4 left over.5/4 = 1 1/4
- Write the answer. This is the answer in its simplest form.1 1/4
Check. Check: 1 1/4 is more than 1, as 5/4 is more than 4/4.
Watch out. A top number bigger than the bottom is more than one whole. Write it as a mixed number.
Method. Line up the decimal points and add in columns. Keep the pound sign and two places for pence.
- Line up the decimal points. Write the pounds and pence in columns.3.46 + 2.85
- Add the pence first. Carry any ten pence into the pounds.46 + 85 = 131 pence
- Add the pounds. Include any carried pounds.3 + 2 = 6 pounds
- Write the answer with the pound sign. Always write two places for the pence.£6.31
Check. Check: £6.31 - £2.85 = £3.46.
Watch out. Always write two digits for the pence: £5.00, not £5.
Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.10:45 to 11:00 is 15 min
- Count the whole hours. Count each full hour after that.1 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.20 min
- Add the parts. Add all the parts for the total time.15 min + 1 h + 20 min = 1 h 35 min
- Write the answer. Give the journey time in hours and minutes.1 h 35 min
Check. Check: 1 h 35 min added to 10:45 gives 12:20.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Watch out
Watch out. 5/4 is 1 1/4, and 10:45 to 12:20 is 1 h 35 min. Check your answer makes sense.
Exam tip
Grown-up tip. Make a short list of the key rules: fractions, decimals, units and time. Practise one list each day.
Exercise 10C Mixed practice: fractions, measures, time and money
Non-calculatorMethod. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.14:24 to 15:00 is 36 min
- Count the whole hours. Count each full hour after that.1 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.6 min
- Add the parts. Add all the parts for the total time.36 min + 1 h + 6 min = 1 h 42 min
- Write the answer. Give the journey time in hours and minutes.1 h 42 min
Check. Check: 1 h 42 min added to 14:24 gives 16:06.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Method. Add the top numbers and keep the bottom number. Simplify if you can.
- Add the top numbers. The bottom number stays the same, because the parts are the same size.3 + 2 = 5
- Keep the bottom number 8. The total is counted in the same parts.5/8
- Write the answer. This is the simplest form.5/8
Check. Check: 5/8 is equal to 5/8.
Watch out. Do not add the bottom numbers too. 2/8 + 3/8 is 5/8, not 5/16.
Method. A zero at the end of a decimal does not change its value.
- Add a zero at the end. Adding a zero after the last digit does not change the value.4.8 = 4.80
- Compare the two numbers. The tenths digit and the zero in the hundredths are both empty places.4.80 = 4.8
- Write the answer. They are equal; the zero only shows that there are no hundredths.4.80
Check. Check: 48/10 = 480/100.
Watch out. 0.5 and 0.50 are equal. The zero at the end does not make the number bigger.
Method. Look at the digit after the place you are rounding to, then decide.
- Look at the hundredths digit. This digit decides whether to round up or down.The digit is 1
- Decide. 5 or more: round up. 4 or less: round down.1 is 4 or less, so round down
- Write the rounded number. Make the digits after the rounding place zero, or leave them out.4.8
Check. Check: 4.8 is the closest number with the right number of places to 4.814.
Watch out. Round up only on a 5 or more. Do not drop the zero from the tenths when rounding to tenths.
Method. Hundredths have two places after the decimal point.
- Look at the bottom number. The bottom number 100 means hundredths: two places after the point.59/100
- Write the digits in the two places. 59 hundredths: a 0 in the tenths place, then 59 in the hundredths place.0.59
- Write the answer. The two digits after the point are hundredths.0.59
Check. Check: 0.59 is 59 hundredths, which is 59/100.
Watch out. Keep both places. 7/100 is 0.07, not 0.7.
Method. Multiply the measure by the number of items, then change to mixed units.
- Work out the total in the smallest unit. Each one is 191 cm.191 cm × 3 = 573 cm
- Change back to m and cm. Share the cm into groups of 100.573 cm = 5 m 73 cm
- Write the answer. Give the total in mixed units.5 m 73 cm
Check. Check: 573 ÷ 3 = 191.
Watch out. Multiply in the small unit, then change back at the end.
Method. Subtract the top numbers and keep the bottom number. Simplify if you can.
- Subtract the top numbers. The bottom number stays the same.2 - 1 = 1
- Keep the bottom number 4. The parts are the same size, so the bottom number does not change.1/4
- Write the answer. This is the simplest form.1/4
Check. Check: 1/4 + 1/4 gives 2/4.
Watch out. Do not subtract the bottom numbers. 7/8 - 3/8 is 4/8, which is 1/2.
Method. Multiply by 1,000 to change kilometres into metres.
- Use the rule. 1 kilometre is 1,000 metres.1 km = 1,000 m
- Multiply the kilometres by 1,000. Each kilometre is 1,000 metres.4 × 1,000 = 4,000
- Write the answer with the unit. The unit is metres.4,000 m
Check. Check: 4,000 ÷ 1,000 = 4.
Watch out. Going to a smaller unit makes the number bigger. Multiply.
Method. Subtract the top numbers and keep the bottom number. Simplify if you can.
- Subtract the top numbers. The bottom number stays the same.4 - 3 = 1
- Keep the bottom number 5. The parts are the same size, so the bottom number does not change.1/5
- Write the answer. This is the simplest form.1/5
Check. Check: 1/5 + 3/5 gives 4/5.
Watch out. Do not subtract the bottom numbers. 7/8 - 3/8 is 4/8, which is 1/2.
Method. Change both measures to the same unit, ml, then add, then change back.
- Change both to ml. 1 l = 1,000 ml.2 l 703 ml = 2,703 ml, and 916 ml = 916 ml
- Add the ml. Work with the same unit.2,703 + 916 = 3,619 ml
- Change back to l and ml. Share the ml into groups of 1,000.3,619 = 3 l and 619 ml
- Write the answer. Give the answer in mixed units, as the question was.3 l 619 ml
Check. Check: 3 l 619 ml - 916 ml gives 2 l 703 ml again.
Watch out. Keep the unit with each number. A total of 1,000 ml is 1 l.
Method. Multiply the measure by the number of items, then change to mixed units.
- Work out the total in the smallest unit. Each one is 3,557 g.3,557 g × 3 = 10,671 g
- Change back to kg and g. Share the g into groups of 1,000.10,671 g = 10 kg 671 g
- Write the answer. Give the total in mixed units.10 kg 671 g
Check. Check: 10,671 ÷ 3 = 3,557.
Watch out. Multiply in the small unit, then change back at the end.
Method. Multiply by 10 to change cm into mm.
- Use the rule. 1 cm is 10 mm.1 cm = 10 mm
- Multiply the cm by 10. Each cm has 10 mm.14 × 10 = 140
- Write the answer with the unit. The unit is mm.140 mm
Check. Check: 140 ÷ 10 = 14.
Watch out. A smaller unit gives a bigger number. Multiply by 10.
Method. Divide by the bottom number to find one part, then multiply by the top number.
- Find one 5th of 15. Share 15 into 5 equal parts.15 ÷ 5 = 3
- Take 2 of those parts. The top number tells us how many parts.2 × 3 = 6
- Write the answer. Keep the unit from the question.6 cm
Check. Check: 3 × 5 = 15, and 2 parts is 6.
Watch out. Divide first, then multiply. Do not multiply by the bottom number.
Method. Write the whole number, then one digit for the tenths and two digits for the hundredths.
- Write the whole number first. This is the part before the decimal point.2
- Write the tenths and the hundredths after the point. 1/10 is one place, and 1/100 is two places.2.11
- Write the answer. Check that each digit is in the right place.2.11
Check. Check: 2.11 = 2 + 0.1 + 0.01, when h is a single digit.
Watch out. Use two places for hundredths. The hundredths digit is the second place after the point.
Method. With the same denominator, compare the numerators.
- Look at the bottom numbers. Both fractions have the same bottom number, so the parts are the same size.Both are 8ths
- Compare the top numbers. With the same size of part, the bigger top number is the bigger fraction.1 and 4
- Choose the greater fraction. The fraction with more parts is greater.4/8
Check. Check: 4 parts is more than 1 parts of the same size.
Watch out. Do not compare the bottom numbers. The bigger the bottom number, the smaller each part.
Method. Hundredths have two places after the decimal point.
- Look at the bottom number. The bottom number 100 means hundredths: two places after the point.46/100
- Write the digits in the two places. 46 hundredths: a 0 in the tenths place, then 46 in the hundredths place.0.46
- Write the answer. The two digits after the point are hundredths.0.46
Check. Check: 0.46 is 46 hundredths, which is 46/100.
Watch out. Keep both places. 7/100 is 0.07, not 0.7.