Lesson 1: Division Expressions with Fractions and Whole Numbers6.NOS.1
Stuck? Start here. Read the steps, try the problem, then check your answer.
I can…
I can explain what dividing with a whole number and a unit fraction means — how many groups fit, or how much is in one group — find the quotient with a model, and check it by multiplying.
Key words
Division of Fractions — Finding how many groups of one fraction fit inside another amount.
Reciprocal — A fraction turned upside down.
Quotient — The answer when you divide.
Dividend — The total number being divided into equal groups (the number inside the division bracket).
Divisor — The number of equal groups you are dividing into (the number outside the division bracket).
Unit fraction — A fraction with 1 on top, like 1/4.
Multiplicative inverse — Two numbers whose product is 1; each is the reciprocal of the other.
Tape diagram — A bar model cut into equal parts to show sharing or grouping.
Steps
I want to cut a 3-foot strip of tape into 1/4-foot pieces, so I write 3 ÷ 1/4. It asks: how many 1/4-foot pieces fit in 3 feet?
Each foot holds 4 quarter-foot pieces, so 3 feet hold 3 × 4 = 12 pieces.
That is why the shortcut works: dividing by 1/4 gives the same answer as multiplying by its reciprocal, 4/1. So 3 ÷ 1/4 = 3/1 × 4/1 = 12. (Some people call this Keep, Change, Flip.)
Check by multiplying: 12 pieces × 1/4 foot = 12/4 = 3 feet. So 3 ÷ 1/4 = 12 pieces.
One more move to know: mixed number → improper fraction: multiply the bottom by the whole number, add the top, keep the same bottom. 3 1/2 → (2 × 3) + 1 = 7 → 7/2.
Try it
What does 4 ÷ 1/3 mean, and what is the quotient? (Think: a 4-foot board cut into 1/3-foot blocks.)
Check your answer
How many 1/3-size pieces fit into 4; quotient is 12
4 ÷ 1/3 means 'how many 1/3-size pieces fit into 4.' Each whole holds 3 thirds, so 4 wholes hold 4 × 3 = 12 thirds. Check: 12 × 1/3 = 4.
Sentence starter
I know ___ because ___.
Goal: I can explain why dividing by a unit fraction gives the same answer as multiplying by its reciprocal, using the words reciprocal, divisor, and quotient.