Division Keywords
When you see these words in a math word problem, they signal that you need to divide. The result is called the quotient. The number being divided is the dividend and the number doing the dividing is the divisor. Any amount left over is the remainder.
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All Division Keywords
divided by
A direct signal to divide one number by another.
Worked Examples
48 divided by 6 is what?
What is 144 divided by 12?
250 divided by 5 equals?
A number divided by 7 equals 13. What is the number?
quotient
The result of dividing one number by another.
Worked Examples
What is the quotient of 44 and 4?
Find the quotient when 120 is divided by 8.
The quotient is 9 and the divisor is 6. What is the dividend?
What is the quotient of 360 and 30?
per
For each one — divide the total by the number of units to find the unit rate.
Worked Examples
A car travels 120 miles per 2 hours. Speed per hour?
5 notebooks cost $20. Cost per notebook?
A 300 g bag of rice costs $1.80. Price per 100 g?
A farmer harvests 2,400 apples from 8 trees. Apples per tree?
each
Every single one receives an equal portion — divide to find the amount per item or person.
Worked Examples
36 apples shared among 9 children. How many does each child get?
48 crayons in 6 equal boxes. How many in each box?
$135 shared equally among 5 people. How much does each receive?
A school has 420 students in 12 classes. Average students per class?
average
The mean value — add all values and divide by how many values there are.
Worked Examples
Find the average of 10, 20, and 30.
A student scored 80, 90, and 70 on three tests. What is the average?
The average rainfall over 5 months was 42 mm. Total rainfall?
Five friends drove 120, 95, 110, 105, and 130 km. Average distance?
half
Divided into two equal parts — divide by 2.
Worked Examples
What is half of 84?
Cut a 50 cm ribbon in half. Length of each piece?
Half of a number is 18. What is the number?
A prize of $5,000 split in half. How much does each winner get?
quarter
Divided into four equal parts — divide by 4.
Worked Examples
What is a quarter of 60?
A quarter of the students are absent. There are 120 students. How many absent?
A quarter of a year is how many months?
A quarter of 200 km is how many kilometres?
split
To divide something into parts.
Worked Examples
Split 72 into 8 equal groups. How many in each group?
A 180 cm plank split into 6 equal pieces. Length of each?
$640 split equally among 8 partners. How much each?
separate
To divide into groups or individual parts.
Worked Examples
Separate 45 marbles into 9 equal groups.
Separate 120 into groups of 15. How many groups?
A class of 36 separated into groups of 4. How many groups?
distribute
To give out equal shares — divide total by number of recipients.
Worked Examples
Distribute 60 pencils equally among 5 classes.
A food bank distributes 840 meals equally across 7 shelters. How many per shelter?
Distribute $3,600 equally among 9 team members.
goes into
How many times one number fits inside another.
Worked Examples
How many times does 11 go into 121?
How many times does 6 go into 90?
How many times does 15 go into 300?
out of
A fraction or proportion — divide the part by the whole.
Worked Examples
8 out of 40 students passed. What fraction is that?
15 out of 60 apples are bruised. What fraction are bruised?
A team won 9 out of 12 games. What fraction did they win?
cut
To divide something physical into pieces of equal or specified size.
Worked Examples
Cut a 90 cm rope into 6 equal pieces. Length of each?
A 240 cm log cut into pieces of 30 cm each. How many pieces?
A 4.5 m ribbon cut into 0.5 m pieces. How many pieces?
ratio
A comparison of two quantities using division.
Worked Examples
The ratio of boys to girls is 3:1. There are 24 boys. How many girls?
A recipe uses flour and sugar in a 4:1 ratio. 200 g flour. How much sugar?
Mix red and blue paint in a 2:3 ratio. 10 ml red. How much blue?
A map scale is 1:25,000. Two points 8 cm apart on map. Real distance?
equal parts
Divided into portions that are all the same size.
Worked Examples
Divide 56 into 7 equal parts.
A 960 ml drink poured into 8 equal parts. How many ml each?
A number split into 5 equal parts gives 13 each. What is the number?
evenly
Without a remainder — divides perfectly so each part is the same size.
Worked Examples
Can 84 be divided evenly by 7?
45 children divided evenly into teams of 9. How many teams?
Does $175 divide evenly among 7 people?
how many times
Asks how often one number fits into another — divide.
Worked Examples
How many times does 5 go into 35?
How many times does 25 fit into 200?
How many times can you subtract 12 from 96?
dividend
The number being divided in a division problem (the total you start with).
Worked Examples
In 48 ÷ 6, identify the dividend.
The quotient is 9 and the divisor is 4. What is the dividend?
The dividend is 150 and the divisor is 6. What is the quotient?
divisor
The number doing the dividing in a division problem.
Worked Examples
In 48 ÷ 6, what is the divisor?
The quotient is 8 and the dividend is 56. What is the divisor?
If the divisor is 12 and the quotient is 5, what is the dividend?
allocate
To assign a specific portion to each recipient — divide to find the portion.
Worked Examples
Allocate 200 minutes of screen time equally across 5 children. Minutes each?
A budget of $18,000 allocated equally to 6 departments. How much per department?
partition
To divide into smaller groups or sections of a specified size.
Worked Examples
Partition 60 students into groups of 12. How many groups?
Partition 240 into sets of 40. How many sets?
how many groups
Asks how many equal groups can be formed — divide total by group size.
Worked Examples
How many groups of 6 can be made from 54 students?
How many groups of 25 can 300 items be divided into?
You have 48 eggs. How many groups of 12 can you fill?
rate
A quantity measured against another unit — divide to find the unit rate.
Worked Examples
A runner completed 10 km in 50 minutes. Rate in km per minute?
A printer prints 180 pages in 6 minutes. Rate per minute?
280 units completed in 4 hours. Rate per hour?
fraction of
A portion of a total — divide numerator by denominator and multiply by the whole.
Worked Examples
What is 1/4 of 80?
A student completed 2/5 of a 50-question test. How many questions done?
Three-quarters of 200 students attend a field trip. How many?
how much each
Asks for the individual share — divide total by number of people or items.
Worked Examples
$84 is split among 7 workers. How much does each worker receive?
180 chocolates are packed into boxes of equal size. There are 9 boxes. How many chocolates in each?
350 km driven by 5 people sharing fuel costs equally. How much each if fuel cost $70?
what is the cost per
Asks for the unit price — divide the total cost by the number of units.
Worked Examples
6 apples cost $3.00. What is the cost per apple?
A 12-pack of water costs $4.80. What is the cost per bottle?
A 5 kg bag of rice costs $8.50. What is the cost per kilogram?