Math / Numbers & Operations

QuestionPractice Find the GCF for each pair of numbers. Use the GCF and the Distributive Property to find the sum of each pair of numbers.
1. 30,100
2. 8.52
3. 28,42
4. 37,67
Use the GCF of the numerator and denominator to simplify each fraction.
5. $\frac{12}{24}$
6. $\frac{18}{112}$
Find the LCM for each pair of numbers. 7.4,9
8. 3, 6
9. 12,5
10. 4, 11

Studdy Solution

STEP 1

1. We need to find the Greatest Common Factor (GCF) for each pair of numbers.
2. Use the GCF and the Distributive Property to find the sum of each pair of numbers.
3. Simplify fractions using the GCF of the numerator and denominator.
4. Find the Least Common Multiple (LCM) for each pair of numbers.

STEP 2

1. Find the GCF for each pair of numbers.
2. Use the GCF and the Distributive Property to find the sum of each pair of numbers.
3. Simplify each fraction using the GCF.
4. Find the LCM for each pair of numbers.

STEP 3

Find the GCF of 30 and 100.
- List the factors of 30: $1, 2, 3, 5, 6, 10, 15, 30$ . - List the factors of 100: $1, 2, 4, 5, 10, 20, 25, 50, 100$ . - The common factors are $1, 2, 5, 10$ . - The GCF is $10$ .

STEP 4

Find the GCF of 8 and 52.
- List the factors of 8: $1, 2, 4, 8$ . - List the factors of 52: $1, 2, 4, 13, 26, 52$ . - The common factors are $1, 2, 4$ . - The GCF is $4$ .

STEP 5

Find the GCF of 28 and 42.
- List the factors of 28: $1, 2, 4, 7, 14, 28$ . - List the factors of 42: $1, 2, 3, 6, 7, 14, 21, 42$ . - The common factors are $1, 2, 7, 14$ . - The GCF is $14$ .

STEP 6

Find the GCF of 37 and 67.
- Since both 37 and 67 are prime numbers, their only common factor is $1$ . - The GCF is $1$ .

STEP 7

Use the GCF and the Distributive Property to find the sum of 30 and 100.
- The GCF is $10$ . - Express each number as a product of the GCF: $30 = 10 \times 3$ , $100 = 10 \times 10$ . - Use the Distributive Property: $10(3 + 10) = 10 \times 13 = 130$ .

STEP 8

Use the GCF and the Distributive Property to find the sum of 8 and 52.
- The GCF is $4$ . - Express each number as a product of the GCF: $8 = 4 \times 2$ , $52 = 4 \times 13$ . - Use the Distributive Property: $4(2 + 13) = 4 \times 15 = 60$ .

STEP 9

Use the GCF and the Distributive Property to find the sum of 28 and 42.
- The GCF is $14$ . - Express each number as a product of the GCF: $28 = 14 \times 2$ , $42 = 14 \times 3$ . - Use the Distributive Property: $14(2 + 3) = 14 \times 5 = 70$ .

STEP 10

Use the GCF and the Distributive Property to find the sum of 37 and 67.
- The GCF is $1$ . - Express each number as a product of the GCF: $37 = 1 \times 37$ , $67 = 1 \times 67$ . - Use the Distributive Property: $1(37 + 67) = 1 \times 104 = 104$ .

STEP 11

Simplify the fraction $\frac{12}{24}$ .
- The GCF of 12 and 24 is $12$ . - Divide the numerator and the denominator by the GCF: $\frac{12}{24} = \frac{12 \div 12}{24 \div 12} = \frac{1}{2}$ .

STEP 12

Simplify the fraction $\frac{18}{112}$ .
- Find the GCF of 18 and 112. - List the factors of 18: $1, 2, 3, 6, 9, 18$ . - List the factors of 112: $1, 2, 4, 7, 8, 14, 16, 28, 56, 112$ . - The common factors are $1, 2$ . - The GCF is $2$ . - Divide the numerator and the denominator by the GCF: $\frac{18}{112} = \frac{18 \div 2}{112 \div 2} = \frac{9}{56}$ .

STEP 13

Find the LCM of 4 and 9.
- List the multiples of 4: $4, 8, 12, 16, 20, 24, 28, 32, 36, 40, \ldots$ . - List the multiples of 9: $9, 18, 27, 36, 45, \ldots$ . - The smallest common multiple is $36$ . - The LCM is $36$ .

STEP 14

Find the LCM of 3 and 6.
- List the multiples of 3: $3, 6, 9, 12, 15, \ldots$ . - List the multiples of 6: $6, 12, 18, 24, \ldots$ . - The smallest common multiple is $6$ . - The LCM is $6$ .

STEP 15

Find the LCM of 12 and 5.
- List the multiples of 12: $12, 24, 36, 48, 60, \ldots$ . - List the multiples of 5: $5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, \ldots$ . - The smallest common multiple is $60$ . - The LCM is $60$ .

STEP 16

Find the LCM of 4 and 11.
- List the multiples of 4: $4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, \ldots$ . - List the multiples of 11: $11, 22, 33, 44, 55, \ldots$ . - The smallest common multiple is $44$ . - The LCM is $44$ .

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Studdy Solution

STEP 1

1. We need to find the Greatest Common Factor (GCF) for each pair of numbers.
2. Use the GCF and the Distributive Property to find the sum of each pair of numbers.
3. Simplify fractions using the GCF of the numerator and denominator.
4. Find the Least Common Multiple (LCM) for each pair of numbers.

STEP 2

1. Find the GCF for each pair of numbers.
2. Use the GCF and the Distributive Property to find the sum of each pair of numbers.
3. Simplify each fraction using the GCF.
4. Find the LCM for each pair of numbers.

STEP 3

Find the GCF of 30 and 100.
- List the factors of 30: $1, 2, 3, 5, 6, 10, 15, 30$ . - List the factors of 100: $1, 2, 4, 5, 10, 20, 25, 50, 100$ . - The common factors are $1, 2, 5, 10$ . - The GCF is $10$ .

STEP 4

Find the GCF of 8 and 52.
- List the factors of 8: $1, 2, 4, 8$ . - List the factors of 52: $1, 2, 4, 13, 26, 52$ . - The common factors are $1, 2, 4$ . - The GCF is $4$ .

STEP 5

Find the GCF of 28 and 42.
- List the factors of 28: $1, 2, 4, 7, 14, 28$ . - List the factors of 42: $1, 2, 3, 6, 7, 14, 21, 42$ . - The common factors are $1, 2, 7, 14$ . - The GCF is $14$ .

STEP 6

Find the GCF of 37 and 67.
- Since both 37 and 67 are prime numbers, their only common factor is $1$ . - The GCF is $1$ .

STEP 7

Use the GCF and the Distributive Property to find the sum of 30 and 100.
- The GCF is $10$ . - Express each number as a product of the GCF: $30 = 10 \times 3$ , $100 = 10 \times 10$ . - Use the Distributive Property: $10(3 + 10) = 10 \times 13 = 130$ .

STEP 8

Use the GCF and the Distributive Property to find the sum of 8 and 52.
- The GCF is $4$ . - Express each number as a product of the GCF: $8 = 4 \times 2$ , $52 = 4 \times 13$ . - Use the Distributive Property: $4(2 + 13) = 4 \times 15 = 60$ .

STEP 9

Use the GCF and the Distributive Property to find the sum of 28 and 42.
- The GCF is $14$ . - Express each number as a product of the GCF: $28 = 14 \times 2$ , $42 = 14 \times 3$ . - Use the Distributive Property: $14(2 + 3) = 14 \times 5 = 70$ .

STEP 10

Use the GCF and the Distributive Property to find the sum of 37 and 67.
- The GCF is $1$ . - Express each number as a product of the GCF: $37 = 1 \times 37$ , $67 = 1 \times 67$ . - Use the Distributive Property: $1(37 + 67) = 1 \times 104 = 104$ .

STEP 11

Simplify the fraction $\frac{12}{24}$ .
- The GCF of 12 and 24 is $12$ . - Divide the numerator and the denominator by the GCF: $\frac{12}{24} = \frac{12 \div 12}{24 \div 12} = \frac{1}{2}$ .

STEP 12

STEP 13

Find the LCM of 4 and 9.
- List the multiples of 4: $4, 8, 12, 16, 20, 24, 28, 32, 36, 40, \ldots$ . - List the multiples of 9: $9, 18, 27, 36, 45, \ldots$ . - The smallest common multiple is $36$ . - The LCM is $36$ .

STEP 14

Find the LCM of 3 and 6.
- List the multiples of 3: $3, 6, 9, 12, 15, \ldots$ . - List the multiples of 6: $6, 12, 18, 24, \ldots$ . - The smallest common multiple is $6$ . - The LCM is $6$ .

STEP 15

Find the LCM of 12 and 5.
- List the multiples of 12: $12, 24, 36, 48, 60, \ldots$ . - List the multiples of 5: $5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, \ldots$ . - The smallest common multiple is $60$ . - The LCM is $60$ .

STEP 16

Find the LCM of 4 and 11.
- List the multiples of 4: $4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, \ldots$ . - List the multiples of 11: $11, 22, 33, 44, 55, \ldots$ . - The smallest common multiple is $44$ . - The LCM is $44$ .

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Studdy Solution

STEP 1

1. We need to find the Greatest Common Factor (GCF) for each pair of numbers.2. Use the GCF and the Distributive Property to find the sum of each pair of numbers.3. Simplify fractions using the GCF of the numerator and denominator.4. Find the Least Common Multiple (LCM) for each pair of numbers.

STEP 2

1. Find the GCF for each pair of numbers.2. Use the GCF and the Distributive Property to find the sum of each pair of numbers.3. Simplify each fraction using the GCF.4. Find the LCM for each pair of numbers.

STEP 3

Find the GCF of 30 and 100.- List the factors of 30: 1,2,3,5,6,10,15,301, 2, 3, 5, 6, 10, 15, 301,2,3,5,6,10,15,30. - List the factors of 100: 1,2,4,5,10,20,25,50,1001, 2, 4, 5, 10, 20, 25, 50, 1001,2,4,5,10,20,25,50,100. - The common factors are 1,2,5,101, 2, 5, 101,2,5,10. - The GCF is 101010.

STEP 4

Find the GCF of 8 and 52.- List the factors of 8: 1,2,4,81, 2, 4, 81,2,4,8. - List the factors of 52: 1,2,4,13,26,521, 2, 4, 13, 26, 521,2,4,13,26,52. - The common factors are 1,2,41, 2, 41,2,4. - The GCF is 444.

STEP 5

Find the GCF of 28 and 42.- List the factors of 28: 1,2,4,7,14,281, 2, 4, 7, 14, 281,2,4,7,14,28. - List the factors of 42: 1,2,3,6,7,14,21,421, 2, 3, 6, 7, 14, 21, 421,2,3,6,7,14,21,42. - The common factors are 1,2,7,141, 2, 7, 141,2,7,14. - The GCF is 141414.

STEP 6

Find the GCF of 37 and 67.- Since both 37 and 67 are prime numbers, their only common factor is 111. - The GCF is 111.

STEP 7

STEP 8

Use the GCF and the Distributive Property to find the sum of 8 and 52.- The GCF is 444. - Express each number as a product of the GCF: 8=4×28 = 4 \times 28=4×2, 52=4×1352 = 4 \times 1352=4×13. - Use the Distributive Property: 4(2+13)=4×15=604(2 + 13) = 4 \times 15 = 604(2+13)=4×15=60.

STEP 9

STEP 10

STEP 11

Simplify the fraction 1224\frac{12}{24}2412​.- The GCF of 12 and 24 is 121212. - Divide the numerator and the denominator by the GCF: 1224=12÷1224÷12=12\frac{12}{24} = \frac{12 \div 12}{24 \div 12} = \frac{1}{2}2412​=24÷1212÷12​=21​.

STEP 12

STEP 13

STEP 14

Find the LCM of 3 and 6.- List the multiples of 3: 3,6,9,12,15,…3, 6, 9, 12, 15, \ldots3,6,9,12,15,…. - List the multiples of 6: 6,12,18,24,…6, 12, 18, 24, \ldots6,12,18,24,…. - The smallest common multiple is 666. - The LCM is 666.

STEP 15

STEP 16

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1. We need to find the Greatest Common Factor (GCF) for each pair of numbers.
2. Use the GCF and the Distributive Property to find the sum of each pair of numbers.
3. Simplify fractions using the GCF of the numerator and denominator.
4. Find the Least Common Multiple (LCM) for each pair of numbers.

1. Find the GCF for each pair of numbers.
2. Use the GCF and the Distributive Property to find the sum of each pair of numbers.
3. Simplify each fraction using the GCF.
4. Find the LCM for each pair of numbers.

Find the GCF of 30 and 100.
- List the factors of 30: $1, 2, 3, 5, 6, 10, 15, 30$ . - List the factors of 100: $1, 2, 4, 5, 10, 20, 25, 50, 100$ . - The common factors are $1, 2, 5, 10$ . - The GCF is $10$ .

Find the GCF of 8 and 52.
- List the factors of 8: $1, 2, 4, 8$ . - List the factors of 52: $1, 2, 4, 13, 26, 52$ . - The common factors are $1, 2, 4$ . - The GCF is $4$ .

Find the GCF of 28 and 42.
- List the factors of 28: $1, 2, 4, 7, 14, 28$ . - List the factors of 42: $1, 2, 3, 6, 7, 14, 21, 42$ . - The common factors are $1, 2, 7, 14$ . - The GCF is $14$ .

Find the GCF of 37 and 67.
- Since both 37 and 67 are prime numbers, their only common factor is $1$ . - The GCF is $1$ .

Use the GCF and the Distributive Property to find the sum of 8 and 52.
- The GCF is $4$ . - Express each number as a product of the GCF: $8 = 4 \times 2$ , $52 = 4 \times 13$ . - Use the Distributive Property: $4(2 + 13) = 4 \times 15 = 60$ .

Simplify the fraction $\frac{12}{24}$ .
- The GCF of 12 and 24 is $12$ . - Divide the numerator and the denominator by the GCF: $\frac{12}{24} = \frac{12 \div 12}{24 \div 12} = \frac{1}{2}$ .

Find the LCM of 3 and 6.
- List the multiples of 3: $3, 6, 9, 12, 15, \ldots$ . - List the multiples of 6: $6, 12, 18, 24, \ldots$ . - The smallest common multiple is $6$ . - The LCM is $6$ .