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Simplifying Monomial Fractions with Products — Easy Worksheet 2
Grade 8 · Whoobee Name: ____________________ Date: __________
Simplify. Multiply first, then divide. Use positive exponents only. Type a fraction with brackets around the bottom, like 1/(6x^3 y^2).
How to solve
First multiply the factors on the top and on the bottom: multiply the numbers and add the exponents of each letter, so 3x3 y3 · 2y = 6x3 y4. Then divide: simplify the numbers, and for each letter subtract the smaller exponent from the bigger one. The letter stays on whichever side had more. So y23x3 y3 · 2y = y26x3 y4 = 16x3 y2.
Example
a2a2 · a5 = ___
Answer: 1a5
Not quite. The answer is
💡 Multiply the bottom first: multiply the numbers: 5 × 4 = 20, and add the exponents of a: 5 + 2 = 7. The bottom is 20a7. The numbers 120 don't simplify, so 1 stays on top and 20 on the bottom. a: 2 on top and 7 on the bottom. The bottom has more: 7 − 2 = 5, so a5 goes on the bottom. So a25a5 · 4a2 = 120a5.
✓ Correct!
Not quite. The answer is
💡 Multiply the bottom first: multiply the numbers: 5 × 4 = 20, and add the exponents of a: 5 + 2 = 7. The bottom is 20a7. The numbers 120 don't simplify, so 1 stays on top and 20 on the bottom. a: 2 on top and 7 on the bottom. The bottom has more: 7 − 2 = 5, so a5 goes on the bottom. So a25a5 · 4a2 = 120a5.
💡 How to solve: Simplifying Monomial Fractions with Products
First multiply the factors on the top and on the bottom: multiply the numbers and add the exponents of each letter, so 3x3 y3 · 2y = 6x3 y4. Then divide: simplify the numbers, and for each letter subtract the smaller exponent from the bigger one. The letter stays on whichever side had more. So y23x3 y3 · 2y = y26x3 y4 = 16x3 y2.
Try a similar one
x6x5 · 4x2 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A letter with no exponent written has exponent 1. Multiply the bottom first: add the exponents of n: 3 + 3 = 6. The bottom is 3n6. The numbers 13 don't simplify, so 1 stays on top and 3 on the bottom. n: 1 on top and 6 on the bottom. The bottom has more: 6 − 1 = 5, so n5 goes on the bottom. So n3n3 · n3 = 13n5.
✓ Correct!
Not quite. The answer is
💡 A letter with no exponent written has exponent 1. Multiply the bottom first: add the exponents of n: 3 + 3 = 6. The bottom is 3n6. The numbers 13 don't simplify, so 1 stays on top and 3 on the bottom. n: 1 on top and 6 on the bottom. The bottom has more: 6 − 1 = 5, so n5 goes on the bottom. So n3n3 · n3 = 13n5.
💡 How to solve: Simplifying Monomial Fractions with Products
First multiply the factors on the top and on the bottom: multiply the numbers and add the exponents of each letter, so 3x3 y3 · 2y = 6x3 y4. Then divide: simplify the numbers, and for each letter subtract the smaller exponent from the bigger one. The letter stays on whichever side had more. So y23x3 y3 · 2y = y26x3 y4 = 16x3 y2.
Try a similar one
y4y4 · 4y2 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A letter with no exponent written has exponent 1. Multiply the bottom first: multiply the numbers: 2 × 3 = 6, and add the exponents of x: 4 + 1 = 5. The bottom is 6x5. The numbers 16 don't simplify, so 1 stays on top and 6 on the bottom. x: 2 on top and 5 on the bottom. The bottom has more: 5 − 2 = 3, so x3 goes on the bottom. So x22x4 · 3x = 16x3.
✓ Correct!
Not quite. The answer is
💡 A letter with no exponent written has exponent 1. Multiply the bottom first: multiply the numbers: 2 × 3 = 6, and add the exponents of x: 4 + 1 = 5. The bottom is 6x5. The numbers 16 don't simplify, so 1 stays on top and 6 on the bottom. x: 2 on top and 5 on the bottom. The bottom has more: 5 − 2 = 3, so x3 goes on the bottom. So x22x4 · 3x = 16x3.
💡 How to solve: Simplifying Monomial Fractions with Products
First multiply the factors on the top and on the bottom: multiply the numbers and add the exponents of each letter, so 3x3 y3 · 2y = 6x3 y4. Then divide: simplify the numbers, and for each letter subtract the smaller exponent from the bigger one. The letter stays on whichever side had more. So y23x3 y3 · 2y = y26x3 y4 = 16x3 y2.
Try a similar one
b35b3 · 3b3 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A letter with no exponent written has exponent 1. Multiply the bottom first: multiply the numbers: 2 × 2 = 4, and add the exponents of a: 1 + 1 = 2. The bottom is 4a2. The numbers 14 don't simplify, so 1 stays on top and 4 on the bottom. a: 1 on top and 2 on the bottom. The bottom has more: 2 − 1 = 1, so a goes on the bottom. So a2a · 2a = 14a.
✓ Correct!
Not quite. The answer is
💡 A letter with no exponent written has exponent 1. Multiply the bottom first: multiply the numbers: 2 × 2 = 4, and add the exponents of a: 1 + 1 = 2. The bottom is 4a2. The numbers 14 don't simplify, so 1 stays on top and 4 on the bottom. a: 1 on top and 2 on the bottom. The bottom has more: 2 − 1 = 1, so a goes on the bottom. So a2a · 2a = 14a.
💡 How to solve: Simplifying Monomial Fractions with Products
First multiply the factors on the top and on the bottom: multiply the numbers and add the exponents of each letter, so 3x3 y3 · 2y = 6x3 y4. Then divide: simplify the numbers, and for each letter subtract the smaller exponent from the bigger one. The letter stays on whichever side had more. So y23x3 y3 · 2y = y26x3 y4 = 16x3 y2.
Try a similar one
y26y3 · 6y3 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Multiply the bottom first: add the exponents of x: 2 + 3 = 5. The bottom is 4x5. The numbers 14 don't simplify, so 1 stays on top and 4 on the bottom. x: 3 on top and 5 on the bottom. The bottom has more: 5 − 3 = 2, so x2 goes on the bottom. So x3x2 · 4x3 = 14x2.
✓ Correct!
Not quite. The answer is
💡 Multiply the bottom first: add the exponents of x: 2 + 3 = 5. The bottom is 4x5. The numbers 14 don't simplify, so 1 stays on top and 4 on the bottom. x: 3 on top and 5 on the bottom. The bottom has more: 5 − 3 = 2, so x2 goes on the bottom. So x3x2 · 4x3 = 14x2.
💡 How to solve: Simplifying Monomial Fractions with Products
First multiply the factors on the top and on the bottom: multiply the numbers and add the exponents of each letter, so 3x3 y3 · 2y = 6x3 y4. Then divide: simplify the numbers, and for each letter subtract the smaller exponent from the bigger one. The letter stays on whichever side had more. So y23x3 y3 · 2y = y26x3 y4 = 16x3 y2.
Try a similar one
a33a4 · 3a2 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A letter with no exponent written has exponent 1. Multiply the top first: multiply the numbers: 4 × 6 = 24, and add the exponents of n: 2 + 1 = 3. The top is 24n3. Divide the numbers: 24 ÷ 2 = 12. n: 3 on top and 4 on the bottom. The bottom has more: 4 − 3 = 1, so n goes on the bottom. So 4n2 · 6n2n4 = 12n.
✓ Correct!
Not quite. The answer is
💡 A letter with no exponent written has exponent 1. Multiply the top first: multiply the numbers: 4 × 6 = 24, and add the exponents of n: 2 + 1 = 3. The top is 24n3. Divide the numbers: 24 ÷ 2 = 12. n: 3 on top and 4 on the bottom. The bottom has more: 4 − 3 = 1, so n goes on the bottom. So 4n2 · 6n2n4 = 12n.
💡 How to solve: Simplifying Monomial Fractions with Products
First multiply the factors on the top and on the bottom: multiply the numbers and add the exponents of each letter, so 3x3 y3 · 2y = 6x3 y4. Then divide: simplify the numbers, and for each letter subtract the smaller exponent from the bigger one. The letter stays on whichever side had more. So y23x3 y3 · 2y = y26x3 y4 = 16x3 y2.
Try a similar one
x3x · 6x5 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A letter with no exponent written has exponent 1. Multiply the top first: add the exponents of b: 1 + 1 = 2. The top is 2b2. Divide the numbers: 2 ÷ 2 = 1. b: 2 on top and 4 on the bottom. The bottom has more: 4 − 2 = 2, so b2 goes on the bottom. So b · 2b2b4 = 1b2.
✓ Correct!
Not quite. The answer is
💡 A letter with no exponent written has exponent 1. Multiply the top first: add the exponents of b: 1 + 1 = 2. The top is 2b2. Divide the numbers: 2 ÷ 2 = 1. b: 2 on top and 4 on the bottom. The bottom has more: 4 − 2 = 2, so b2 goes on the bottom. So b · 2b2b4 = 1b2.
💡 How to solve: Simplifying Monomial Fractions with Products
First multiply the factors on the top and on the bottom: multiply the numbers and add the exponents of each letter, so 3x3 y3 · 2y = 6x3 y4. Then divide: simplify the numbers, and for each letter subtract the smaller exponent from the bigger one. The letter stays on whichever side had more. So y23x3 y3 · 2y = y26x3 y4 = 16x3 y2.
Try a similar one
n44n4 · 3n5 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A letter with no exponent written has exponent 1. Multiply the top first: multiply the numbers: 2 × 4 = 8, and add the exponents of x: 2 + 1 = 3. The top is 8x3. Simplify the numbers: 86 = 43 (divide both by 2). x: 3 on top and 4 on the bottom. The bottom has more: 4 − 3 = 1, so x goes on the bottom. So 2x2 · 4x6x4 = 43x.
✓ Correct!
Not quite. The answer is
💡 A letter with no exponent written has exponent 1. Multiply the top first: multiply the numbers: 2 × 4 = 8, and add the exponents of x: 2 + 1 = 3. The top is 8x3. Simplify the numbers: 86 = 43 (divide both by 2). x: 3 on top and 4 on the bottom. The bottom has more: 4 − 3 = 1, so x goes on the bottom. So 2x2 · 4x6x4 = 43x.
💡 How to solve: Simplifying Monomial Fractions with Products
First multiply the factors on the top and on the bottom: multiply the numbers and add the exponents of each letter, so 3x3 y3 · 2y = 6x3 y4. Then divide: simplify the numbers, and for each letter subtract the smaller exponent from the bigger one. The letter stays on whichever side had more. So y23x3 y3 · 2y = y26x3 y4 = 16x3 y2.
Try a similar one
m22m2 · 4m4 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Simplifying Monomial Fractions with Products — Easy Worksheet 2
Simplify. Multiply first, then divide. Use positive exponents only. Type a fraction with brackets around the bottom, like 1/(6x^3 y^2).