GCF/LCM
What is the GCF of 4 and 24?
GCF = 4
Factors of 4 = 1,2, 4
Factors of 24 = 1,2,3,4,8,12,24
Is this fraction in simplest form, yes or no?
4/5
Yes
GCF of 4 and 5 is 1
Factors of 4: 1, 2, 4
Factors of 5: 1,5
If the GCF is 1 it is simplified (remember 1 and done)
Solve. Write your answer in simplest form.
1 1/10 + 1 7/10
Answer: 2 4/5 (unsimplified answer = 2 8/10)
1. Add numerators (keep denominator the same)
1/10 + 7/10 =8/10
2. Add whole numbers
1 +1 = 2
3. Simplify. 2 8/10 (GCF is 2, divide numerator and denominator by 2) =
2 4/5
Bob runs 3/4 miles every day after school. How many miles does he run in five days?
Answer: 3 3/4 miles
1. Write the whole number over 1 (5 = 5/1)
2. Multiply numerator x numerator and denominator x denominator
5 x 3 = 15
4 x 1 = 4
3. Simplify 15/4 by dividing 15 divided by 4 = 3 R 3, 3 3/4
Estimate the difference.
4 1/8 - 3/6
Answer: 3
1. Round the mixed number to the nearest whole.
4 1/8 --> closest to 4 (not 5)
5/10 --> closest to 1 (half, round up)
2. Rewrite your expression with your rounded numbers and solve.
4 - 1 = 3
What is the GCF of 4, 12 and 20?
GCF = 4
Factors of 4: 1,2,4
Factors of 12: 1,2,3,4,6,12
Factors of 20: 1,2,4,5,10,20
Is this fraction in simplest form, yes or no?
4/8
No.
The GCF is 4, the numerator and denominator can both be divided by 4 to be simplified to 1/2.
Factors of 4: 1,2,4
Factors of 8: 1,2,4,8
Solve. Write your answer in simplest form.
1 1/3 - 1/4
Answer: 1 1/12
1. Find the LCM of 3 and 4 = 12
2. Rewrite fractions using the LCM as the LCD and multiplying
1/3 x 4/4 = 4/12
1/4 x 3/3 =3/12
3. Subtract numerators, keep denominators
4/12 - 3/12 = 1/12
4. Subtract the whole number
1 - 0 = 1
5. Simplify 1 1/12 (GCF is 1 so it's simplified!)
Multiply. Write your answer in simplest form.
3/5 x 11
Answer: 6 3/5 (unsimplified = 33/5)
1. Rewrite the whole number over 1, 11=11/1
2. Multiply numerator x numerator and denominator x denominator
3 x 11 = 33
5 x 1 = 5
3. Simplify 33/5 by dividing 33 by 5 = 6 R. 5 (quotient is the whole number, remainder is the numerator, keep denominator the same) = 6 3/5
Estimate the sum.
5 8/10 + 2 2/10
Answer: 8
1. Round the mixed number to the nearest whole.
5 8/10 --> closest to 6 (not 5)
2 2/10--> closest to 2 (not 3)
2. Rewrite your expression with your rounded numbers and solve.
6 + 2 = 8
What is the LCM of 2 and 12?
LCM = 12
Multiples of 2: 2, 4, 6, 8, 10, 12....
Multiples of 12: 12, 24....
TIs this fraction in simplest form, yes or no?
3/12
No.
Factors of 3: 1,3
Factors of 12: 1,2,3,4,6,12
The GCF is 3, the numerator and denominator can be divided by 3 to equal 1/4.
Solve. Write your answer in simplest form.
1/2 + 2/4 + 5/8
Answer: 1 5/8 (unsimplified = 13/8)
1. Find the LCM of 2, 4 and 8 = 8
2. Rewrite fractions using the LCM as the LCD using multiplication.
1/2 x 4/4 =4/8
2/4 x 2/2 = 4/8
5/8 (already in 8ths)
3. Add all three at once
4/8 + 4/8 + 5/8 = 13/8
4. Simplify. Make the improper fraction a mixed number by dividing 13 by 8 = 1 R. 5 (quotient is the whole number, remainder is the numerator, denominator stays the same) = 1 5/8 (the GCF is 1 so it's done!)
Divide. Simplify
2/3 divided by 1/5
Answer: 3 1/3 (unsimplified = 10/3)
1. KEEP the first fraction. 2/3
2. CHANGE the division symbol to multiplication.
3. FLIP the fraction upside down to write it as the reciprocal (1/5 is now 5/1)
4. MULTIPLY 2/3 x 5/1 = 10/3
5. Simplify 10/3 = 10 divided by 3 = 3 R. 1 = 3 1/3 (GCF is 1, you're done!)
Estimate.
1/8 + 4/8
Answer: 1
1. Round to the nearest whole.
1/8 --> closest to 0 (not 1)
4/8--> closest to 1 (half, round up)
2. Rewrite your expression with your rounded numbers and solve.
0 + 1
What is the LCM of 5 and 8?
LCM = 40
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40....
Multiples of 8: 8, 16, 24, 32, 40...
Is this fraction in simplest form, yes or no?
3/8
Yes.
Factors of 3: 1,3
Factors of 8: 1,2,4,8
If the GCF is 1 it is simplified (remember, 1 and done)
Solve. Write your answer in simplest form.
5/8 + 3/4
Answer: 1 3/8 (unsimplified = 11/8)
1. Find the LCM of 8 and 4 = 8
2. Rewrite the fractions using the LCM as the new LCD
5/8 (stays 5/8)
3/4 x 2/2 = 6/8
3. Add. 5/8 + 6/8 =11/8
4. Simplify (improper fractions need to be turned into mixed numbers by dividing 11 by 8) 11 divided by 8 = 1 R. 3 (quotient is the whole number, remainder is the numerator, keep the denominator the same) = 1 3/8 (GCF is 1, so you're done)
Sally has a box of Oreos. There are 8 cookies in the box. She eats 1/4. How many cookies did she eat? Write your answer in simplest form.
Answer: 2 cookies (unsimplified = 8/4)
1. Rewrite the whole number as a fraction over 1 (8 = 8/1)
2. Multiply numerator x numerator and denominator x denominator
8 x 1 = 8
1 x 4 = 4
3. Simplify 8/4 = 8 divided by 4 = 2
Estimate
1 4/5 - 3/5
Answer: 1
1. Round the mixed number to the nearest whole.
1 4/5--> closest to 2 (not 1)
3/5 --> closest to 1 (not 0)
2. Rewrite your expression with your rounded numbers and solve.
2-1 = 1
What is the LCM of 2, 4 and 6?
LCM = 12
Multiples of 2: 2, 4, 6, 8, 10, 12...
Multiples of 4: 4, 8, 12....
Multiples of 6: 6, 12....
Is this fraction in simplest form, yes or no?
11/24
Yes.
Factors of 11: 1,11
Factors of 24: 1,2,3,4,6,8,12,24
GCF is 1 (if the GCF is 1 you're done!)
Solve. Write in simplest form.
2 2/12 - 1 4/8
Simplified Answer = 2/3 (unsimplified = 16/24)
1. Find the LCM of 12 & 8 = 24
2. Rewrite the fractions with the LCM as the LCD -->
2 2/12 (x2/2) = 2 4/24
1 4/8 (x3/3) = 1 12/24
3. Subtract 2 4/24 - 1 12/24
4. Regroup (take one away, add a whole) 1 4/24 + 24/24 = 1 28/24
5. Subtract 1 28/24 - 1 12/24 = 16/24
6. Simplify. GCF = 8 (divide numerator and denominator by 8)
Divide. Write in simplest form.
2/5 divided by 3/4
Answer: 8/15
1. KEEP the first fraction 2/5
2. CHANGE the division symbol to multiplication.
3. FLIP the second fraction to rewrite as the reciprocal (3/4 is now 4/3)
4. Multiply
2 x 4 = 8
5 x 3 = 15
5. Simplify 8/15 (GCF is 1, so you're done!)
Joe is driving to his grandmother's house. His grandmother lives 40 4/6 miles away. Joe drives 23 2/6 miles and stops. About how much farther does he have to drive?
Answer: 18 miles
1. Round the mixed number to the nearest whole.
40 4/6 --> closest to 41 (not 40)
23 2/6 --> closest to 23 (not 24)
2. Rewrite your expression with your rounded numbers and solve.
41-23 =18