Step-by-step Maths Level 4: Fractions, time and problems
Part of the Step-by-step Maths Level 4 level 4 check chapter. Chapter overview · whole chapter on one page
Fractions, time and problems
A fraction of an amount: divide by the bottom number, then multiply by the top number.
For time, count the minutes to the next hour, then the whole hours, then the last minutes. In problems, look at the key words first.
Key ideas
- Divide by the bottom number, then multiply by the top.
- Count on in steps to find a duration.
- Key words tell you the operation.
Method. Find one equal part by dividing by the bottom number. Then multiply by the top number.
- Divide 20 into 4 equal parts. The bottom number tells us how many equal parts to make.20 ÷ 4 = 5
- Take 3 of the parts. The top number tells us how many parts to take.3 × 5 = 15
- Write the answer. This is the fraction of the amount.15
Check. Check: 5 + 5 + 5 = 15, and the last part is 5.
Watch out. Divide by the bottom number first, then multiply by the top.
Method. Count on from the start time to the end time, in steps: minutes to the hour, whole hours, then minutes.
- Count the minutes to the next hour. Count on to 15:00.20 to 14:20 is 40 minutes to 15:00
- Count the minutes after the hour. Count on from 15:00 to 15:05.5 minutes
- Add the parts. Add the minutes together.40 + 5 = 45
- Write the duration. The duration is 45 minutes.45 minutes
Check. Check: 14:20 plus 45 minutes is 15:05.
Watch out. Count on in minutes, not in hours.
Method. Solve in two steps: multiply, then add. Check the first step before the second.
- Find the first step. The packs have equal groups, so multiply.4 × 25 = 100
- Find the second step. Add the loose stickers to the total of the packs.100 + 13 = 113
- Write the answer. This is the total altogether.113
Check. Check: 113 - 13 = 100, and 100 is 4 packs of 25.
Watch out. Do the first step, write the answer, then use it in the second step.
Watch out
Watch out. 3/4 of 20 is 15, not 5. Find one quarter, then take three quarters.
Exam tip
Grown-up tip. Make a short list: the times tables, the fractions and the units. Practise one list each day.
Exercise 10C Mixed practice: fractions, time and problems
Non-calculatorMethod. Use the facts: 60 minutes in an hour, 24 hours in a day, and the number of days in each month.
- Think about the calendar month of August. Months have 28, 30 or 31 days. February is left out here.August has 31 days
- Count the days. Count all the days in the month.31 days
- Write the answer. This is the number of days in the month.31
Check. Check the fact: 60 minutes, 24 hours, or the days in the month.
Watch out. Learn the months with 30 days: April, June, September and November. All the others have 31 days, except February.
Method. Add the length of the activity to the start time. Carry extra minutes into the hours.
- Write the start time. It is where we begin.12:34
- Add the duration. Add 1 hour 45 minutes to the start time.12:34 + 1 hour 45 minutes = 14:19
- Write the finish time. Use two digits for the hour and minutes.14:19
Check. Check: 1 hour 45 minutes before 14:19 is 12:34.
Watch out. When the minutes go past 60, add one hour and take away 60 minutes.
Method. Write the parts chosen on top, and the total number of equal parts on the bottom.
- Find the number of equal parts in the whole. The whole is split into this many equal parts.10 equal parts
- Find the number of parts chosen. These are the parts we count on the top.7 parts
- Write the fraction. Parts chosen over total parts.7/10
Check. Check: 7 of the 10 parts is 7/10.
Watch out. The top number is never bigger than the bottom number for a fraction of one whole.
Method. Count on from the start time to the end time, in steps: minutes to the next hour, whole hours, then minutes.
- Count the whole hours up to 08:00. Each full hour is 60 minutes.2 hours = 120 minutes
- Count the minutes from 08:00 to 08:51. Count on the last minutes.51 minutes
- Add the parts. Add the minutes from each part.0 + 120 + 51 = 171
- Write the duration. Give the answer in hours and minutes.2 hours 51 minutes
Check. Check: 06:00 plus 2 hours 51 minutes is 08:51.
Watch out. Count the minutes to the next hour first. Do not subtract the hours and the minutes separately.
Method. Equal bars show equal fractions. Count the equal parts in the second bar.
- Look at the first bar. It has shaded parts out of equal parts.1 shaded of 2
- Look at the second bar. It has twice as many parts, and twice as many shaded.2 shaded of 4
- Write the missing number. The bottom number is the total parts in the second bar.4
Check. Check: 2/4 is the same as 1/2.
Watch out. Doubling the top and bottom gives an equal fraction.
Method. Find the key words, choose the operation (division), then work out the answer.
- Find the key words. “shared equally” means the same number in each group.455 into 5 groups
- Choose the operation. Sharing into equal groups is division.455 ÷ 5
- Work out the answer. Ask: how many groups of 5 make 455?5 × 91 = 455
- Write the answer. This is the number for each child.91
Check. Check the answer with the opposite operation to make sure it fits the story.
Watch out. Read the question for the key words first. Then choose the operation before you work out the answer.
Method. Find the key words, choose the operation (subtraction), then work out the answer.
- Find the key words. “sold” and “left” mean some are taken away.3008 and 1710
- Choose the operation. Taking away is subtraction.3008 - 1710
- Work out the answer. Use exchange if a column is too small.3008 - 1710 = 1298
- Write the answer. This is how many are left.1298
Check. Check the answer with the opposite operation to make sure it fits the story.
Watch out. Read the question for the key words first. Then choose the operation before you work out the answer.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 260 ÷ 10. The bottom number tells how many equal parts.260 ÷ 10 = 26
- Take 6 parts. The top number tells how many parts are blue.6 × 26 = 156
- Write the answer. This is the number of blue ones.156
Check. Check: the parts given and the parts left make 260.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.2 equal parts
- Count the shaded parts. The top number is the number of shaded parts.1 shaded parts
- Write the fraction. Shaded parts over the total number of parts.1/2
Check. Check: 1 + 1 = 2, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. Find the key words, choose the operation (subtraction), then work out the answer.
- Find the key words. “sold” and “left” mean some are taken away.5533 and 4416
- Choose the operation. Taking away is subtraction.5533 - 4416
- Work out the answer. Use exchange if a column is too small.5533 - 4416 = 1117
- Write the answer. This is how many are left.1117
Check. Check the answer with the opposite operation to make sure it fits the story.
Watch out. Read the question for the key words first. Then choose the operation before you work out the answer.
Method. Equivalent fractions: multiply or divide the top and bottom by the same number.
- Divide the top number by 2. Divide the top and the bottom by the same number.2 ÷ 2 = 1
- Divide the bottom number by 2. The fraction keeps the same value.8 ÷ 2 = 4
- Write the missing number. This is the top number of the simpler fraction.1
Check. Check: 2/8 and 1/4 are equal.
Watch out. Do the same to the top and the bottom. Never change one and not the other.
Method. Count on from the start time to the end time, in steps: minutes to the next hour, whole hours, then minutes.
- Count the minutes to the next hour, 12:00. Count on to the next full hour.11:52 to 12:00 is 8 minutes
- Count the whole hours up to 13:00. Each full hour is 60 minutes.1 hour = 60 minutes
- Count the minutes from 13:00 to 13:17. Count on the last minutes.17 minutes
- Add the parts. Add the minutes from each part.8 + 60 + 17 = 85
- Write the duration. Give the answer in hours and minutes.1 hour 25 minutes
Check. Check: 11:52 plus 1 hour 25 minutes is 13:17.
Watch out. Count the minutes to the next hour first. Do not subtract the hours and the minutes separately.
Method. Solve in two steps: multiply, then add. Check the first step before the second.
- Find the first step. The packs have equal groups, so multiply.8 × 21 = 168
- Find the second step. Add the loose ones to the total of the packs.168 + 12 = 180
- Write the answer. This is the total altogether.180
Check. Check: work backwards from your answer to see if the story makes sense.
Watch out. In a two-step problem, do the first step, write the answer, then use it in the second step.
Method. A fraction is the number of shaded parts over the number of equal parts.
- Count the equal parts in the whole. The bottom number is the number of equal parts.3 equal parts
- Count the shaded parts. The top number is the number of shaded parts.2 shaded parts
- Write the fraction. Shaded parts over the total number of parts.2/3
Check. Check: 2 + 1 = 3, so the other parts are not shaded.
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. Find one equal part by dividing by the bottom number. Then multiply by the top number.
- Divide 32 into 4 equal parts. The bottom number tells us how many equal parts to make.32 ÷ 4 = 8
- Take 1 of the parts. The top number tells us how many parts to take.1 × 8 = 8
- Write the answer. This is the fraction of the amount.8
Check. Check: 3 parts are left and 24 is left over, so 8 + 24 = 32.
Watch out. Divide by the bottom number first, then multiply by the top number.
Method. There are 60 minutes in an hour. Multiply hours by 60 to change to minutes, or divide minutes by 60 to change to hours.
- Change 5 hours to minutes. There are 60 minutes in 1 hour.5 × 60 = 300
- Add the minutes. Put the extra minutes on the end.300 + 30 = 330
- Write the answer. This is the total number of minutes.330
Check. Check: 5 hours is 300 minutes, and 30 more is 330.
Watch out. Do not write 2 hours 135 minutes. Change every 60 minutes into 1 hour.