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Week 04 · Dividing Fractions

Friday

Division all around
// How many pieces fit, and how much is in each
⏱ about 20 min

Friday: Division All Around

Rocket pins the Field Day schedule to the wall. "Three hours. Each game lasts half an hour. How many games?"

"That is 3 ÷ 1/2," says Raven. "What do you notice?"

"Six games," Rocket says. "Two halves in every hour, three hours."

"And practice is 1 1/2 hours, in quarter-hour turns," Raven adds. "How many turns?"

Rocket writes 3/2 ÷ 1/4 = 3/2 × 4 = 6. "Six turns. Division is everywhere today."

Nova hovers over the schedule. "It was everywhere all week," she says. "Scoops, strips, ribbon, signs."

Rocket grins. "And next week? What do you divide next?"

Nova hums. "Numbers with a decimal point. Bring the tape measure."

Fractions you divide every day

Time: how many half-hour games fit in 3 hours? 3 ÷ 1/2 = 6.

Recipes: how many 1/4 cup scoops make 1 1/2 cups? 1 1/2 ÷ 1/4 = 6.

Walking: a 2 1/2 mile trail in 1/2 mile sections has 2 1/2 ÷ 1/2 = 5 sections.

Sharing: 3/4 of a strip of stickers shared among 3 friends gives 3/4 ÷ 3 = 1/4 strip each.

Check before you flip

Dividing by a fraction less than 1 gives a quotient bigger than the dividend. 5 ÷ 1/3 = 15.

Dividing by a number bigger than 1 gives a quotient smaller than the dividend. 5 ÷ 3 is less than 2.

Dividing by 1 changes nothing. Use these checks to catch a flipped mistake before it spreads.

EVERYDAY DIVISION
  • Read the question.
  • Tap your answer.
Field Day runs 3 hours, with half-hour games. How many games?
Practice lasts 1 1/2 hours in 1/4 hour turns. How many turns?
A 2 1/2 mile trail is marked in 1/2 mile sections. How many sections?
A 4 meter banner is divided into 2/3 meter panels. How many panels?
BIGGER OR SMALLER?
  • Read the question.
  • Tap your answer.
Without working it out: is 5 ÷ 1/3 bigger or smaller than 5?
Without working it out: is 3/4 ÷ 2 bigger or smaller than 3/4?
Without working it out: is 2/3 ÷ 1/6 bigger or smaller than 2/3?
Without working it out: is 7 ÷ 1 bigger or smaller than 7?
DIVIDE 5/6 ÷ 2/3, STEP BY STEP
  • ?Simplify: 15/12 = 1 1/4
  • ?Multiply across: 5/6 × 3/2 = 15/12
  • ?Flip the divisor: 2/3 becomes 3/2
  • ?Write the problem: 5/6 ÷ 2/3
WHY THIS EXERCISEThe order of the steps is the method. Simplifying at the end keeps the fractions easy to read.
Week reviewTrue or false?
3 ÷ 1/2 = 6?
2/3 ÷ 3/4 = 8/9?
3/4 ÷ 3 = 1/4?
5 ÷ 1/3 = 5/3?
Dividing by a fraction less than 1 makes the quotient bigger than the dividend.?
WHY THIS EXERCISE5 ÷ 1/3 is 15, not 5/3. Flipping the dividend instead of the divisor is the slip to watch for.
Try it
Find a clock. Count how many 1/4 hour turns fit in 2 hours, and write the division sentence.
Find a measuring cup. Count how many 1/2 cups fit in 3 cups of water, and write that sentence too.
Draw the Field Day schedule as a number line from 0 to 3 hours, marked in half-hour games.

A whole week of fraction division. Tomorrow is Data Day: a scoop count with your family.

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