Lesson 3 of 10 · Chapter 3
The Pet Shop Owner
You own Paws & Fins Pet Shop. In this lesson you name fractions, find equivalent fractions and simplify them, compare fractions, and add and subtract them, to feed the animals, clean the tanks and run the shop.
Choose how you want to learn
You can change this any time. Press Listen on any part to hear it read aloud. Grown-ups: read along with younger children.
- 1 · What a fraction is
- 2 · Equivalent fractions
- 3 · Comparing fractions
- 4 · Adding and subtracting
- 5 · Fractions of a group
- 6 · The whole chapter
- 7 · Try it at home
- 8 · Your card
- 9 · Check yourself
Part 1
What a fraction is
A fraction names part of a whole that is cut into equal parts.
The bottom number, the denominator, says how many equal parts there are. The top number, the numerator, says how many you have.
In 3/8 you have 3 parts out of 8.
A cage has 6 equal compartments and 4 hold hamsters: 4/6 have hamsters and 2/6 are empty. Together 4/6 + 2/6 = 6/6, one whole cage.
Fractions also name part of a group. Of 12 puppies, 7 are brown: 7/12 are brown and 5/12 are white.
And they name what is missing. A bag 3/4 full is 1/4 empty, because a full bag is 4/4.
“Numerator (top): The number of parts you have”
“Denominator (bottom): The total number of equal parts”
“In 3/8: You have 3 parts out of 8 total equal parts.”
What fraction of the bar is gold? Type it like 3/8. Five right to finish.
Part 2
Equivalent fractions
Equivalent fractions look different but mean the same amount. 2/4 and 1/2 are the same amount of pizza.
Multiply or divide the top and bottom by the same number, and the amount stays the same.
To simplify 8/12, find a number that divides both: 4. 8 ÷ 4 = 2 and 12 ÷ 4 = 3, so 8/12 = 2/3.
To find a missing number, 3/4 = ?/12: what times 4 makes 12? Three. Do the same to the top: 3 × 3 = 9. So 3/4 = 9/12.
A fraction is in simplest form when no number bigger than 1 divides both top and bottom.
“Equivalent fractions are different fractions that represent the same amount.”
“Simplified: 8/12 = 2/3”
Find the missing number, or simplify. Five right to finish.
Part 3
Comparing fractions
When two fractions have the same bottom number, compare the tops: 5/8 is more than 3/8.
When the bottoms are different, turn them into the same bottom number first.
3/4 or 2/3? A common denominator of 4 and 3 is 12. 3/4 = 9/12 and 2/3 = 8/12. Since 9/12 is more than 8/12, 3/4 > 2/3.
When the top numbers match, look at the size of the pieces. Fifths are bigger pieces than sevenths, because the whole is cut into fewer parts. So 2/5 is more than 2/7: same number of pieces, bigger pieces.
“Method: Find a common denominator”
“Same numerator: Larger denominator = smaller fraction”
Which is bigger? Look at the bars, then tap <, > or =. Five right to finish.
Part 4
Adding and subtracting fractions
When the bottom numbers match, add or subtract the top numbers. The bottom number stays the same.
1/4 + 2/4 = 3/4.
When they do not match, make them match first.
2/3 + 1/6: sixths fit both, so change 2/3 into 4/6. Then 4/6 + 1/6 = 5/6.
A tank is 7/8 full and you use 1/4 for a water change. Change 1/4 into 2/8. Then 7/8 − 2/8 = 5/8 of the tank remains.
Never add the bottom numbers. Eighths plus eighths are still eighths.
“When denominators match, just add the numerators:”
“The denominator stays the same!”
Add or subtract. Any equal fraction counts, but try for simplest form. Five right to finish.
Part 5
Fractions of a group
To find a fraction of a group, split the group into equal parts and count one part.
1/3 of 24 animals: split 24 into 3 equal groups of 8. So 1/3 of 24 is 8.
The bottom number tells how many equal groups to make. The top number tells how many of those groups to count. 3/4 of 24 is three groups of 6, which is 18.
Shop owners use this every day: if 1/4 of 24 animals are cats, that is 6 cats to feed.
“INVENTORY: 24 animals total. 1/3 are dogs, 1/4 are cats. How many dogs? How many cats?”
How many animals is that? Look at the picture, then type the number. Three right to finish.
Part 6
Read the whole chapter
Here is all of Chapter 3, “The Pet Shop Owner”, exactly as the book tells it, with every worked example, all 69 practice problems and the Action Report. Press Listen to hear it read aloud, or open it and work along with a pencil.
Open Chapter 3
Part 7
Try it at home
Do these with your family. Tick each one when it is done.
Part 8
Your “Pet Shop Owner” card
Fill it in, then print it for the fridge. Nothing you type here leaves this device.
Pet Shop Owner’s Card
Global Sovereign University · Grade 4 Mathematics, lesson 3
Fraction rules
- Bottom: how many equal parts. Top: how many you have.
- Same change top and bottom keeps the amount.
- Compare and add only with the same bottom number.
- Never add the bottom numbers.
Part 9
Check yourself
6 questions. Pick an answer. If it is not right, read the hint and try again.
Lesson 3 complete.
You can name fractions, find equivalent fractions and simplify them, compare fractions, add and subtract them, and find a fraction of a group. Next: Lesson 4, The Recipe Master. Back to the class.
Homeschooling Math Books for Kids: Grade 4 by Dr. Gene A Constant. This lesson is Chapter 3, and the whole chapter is on this page.
GSU is a 501(c)(3) nonprofit and book sales are its only income. A purchase is not a tax-deductible donation. This lesson is free and always will be.