Step: 1

The cookies left over = 5 1 3 - 3 5 6

Step: 2

= 5 2 6 - 3 5 6

[Write an equivalent fraction for 1 3 with LCD 6 as denominator.]

Step: 3

= 4 8 6 - 3 5 6

[Since 5 6 > 2 6 , rewrite 5 2 6 as 4 + 1 2 6 = 4 8 6 .]

Step: 4

= (4 - 3) + (8 6 - 5 6 )

[Subtract the whole numbers and fractions.]

Step: 5

= 1 3 6

Step: 6

11 2 lb of cookies were left.

Correct Answer is : 11 2 lb

Step: 1

The corn chips left = 6 1 3 - 2 1 5

Step: 2

= (6 - 2) + (1 3 - 1 5 )

[Separate the whole numbers and fractions.]

Step: 3

= (6 - 2) + (5 15 - 3 15 )

[Rewrite the fractions with same denominator.]

Step: 4

= 4 + 2 15

[Subtract the whole numbers and fractions.]

Step: 5

= 4 2 15

[Simplify the fraction and combine the two terms.]

Step: 6

Correct Answer is : 4 2 15 lb

Step: 1

The milk left = 9 5 6 - 5 2 3

Step: 2

= (9 - 5) + (5 6 - 2 3 )

[Separate whole numbers and the fractions.]

Step: 3

= (9 - 5) + (5 6 - 4 6 )

[Use LCD 6 to rewrite the fractions with same denominator and subtract.]

Step: 4

= 4 + 1 6

[Subtract the whole numbers and the fractions.]

Step: 5

= 4 1 6

[Simplify the fraction and combine the two terms.]

Step: 6

The milk left is 4 1 6 gallons.

Correct Answer is : 4 1 6

Step: 1

[Write expression for the difference between the lengths.]

Step: 2

= (5 - 2) + (3 4 - 2 3 )

[Write the whole numbers and the fractions separately.]

Step: 3

= (5 - 2) + (9 12 - 8 12 )

[Rewrite the fractions with same denominator using the L.C.D, 12.]

Step: 4

= 3 + 1 12

[Add.]

Step: 5

= 3 1 12

[Write the sum as mixed number.]

Step: 6

The length of the rope remaining is 3 1 12 in.

Correct Answer is : 3 1 12 in.

Step: 1

[Original expression.]

Step: 2

= 42 1 30 - 30 12 30

[Use LCD 30 to write the equivalent fraction of 2 5 .]

Step: 3

= 41 31 30 - 30 12 30

[Since 1 30 < 12 30 , rewrite 42 1 30 as 41 + 1 1 30 = 41 31 30 .]

Step: 4

= (41 - 30) + (31 30 - 12 30 )

[Write the whole numbers and fractions separately.]

Step: 5

= 11 + 19 30

[Subtract the whole numbers and fractions.]

Step: 6

= 1119 30

[Combine the two terms.]

Step: 7

The difference of 42 1 30 and 30 2 5 is 1119 30 .

Correct Answer is : 1119 30

Step: 1

Total quantity of mixture = 3 1 3 cups

Step: 2

Amount of milk in the mixture = 2 1 4 cups

Step: 3

Amount of water in the mixture = Amount of total mixture - Amount of milk in the mixture

Step: 4

= 3 1 3 cups - 2 1 4 cups

Step: 5

= 3 4 12 - 2 3 12

[Multiply the numerator and denominator of 1 3 with 4 and 1 4 with 3 to make the denominators equal.]

Step: 6

= 1 1 12

[Subtract whole numbers and subtract fractions.]

Step: 7

So, 1 1 12 cups of water is added in the mixture.

Correct Answer is : 1 1 12 cups

Step: 1

The cookies left over = 7 1 3 - 4 5 6

Step: 2

= 7 2 6 - 4 5 6

[Write an equivalent fraction for 1 3 with LCD 6 as denominator.]

Step: 3

= 6 8 6 - 4 5 6

[Since 5 6 > 2 6 , rewrite 7 2 6 as 6 + 1 2 6 = 6 8 6 .]

Step: 4

= (6 - 4) + (8 6 - 5 6 )

[Subtract the whole numbers and fractions.]

Step: 5

= 2 3 6

Step: 6

21 2 lb cookies were left.

Correct Answer is : 21 2 lb

Step: 1

The cookies left = 6 1 5 - 4 1 7

Step: 2

(6 - 4) + (1 5 - 1 7 )

[Separate the whole numbers and fractions.]

Step: 3

= (6 - 4) + (7 35 - 5 35 )

[Rewrite the fractions with same denominator.]

Step: 4

= 2 + 2 35

[Subtract the whole numbers and fractions.]

Step: 5

= 2 2 35

[Simplify the fraction and combine the two terms.]

Step: 6

Correct Answer is : 2 2 35 lb

Step: 1

[Original expression.]

Step: 2

= 7 2 4 - 3 1 4

[Rewrite the fractional part in the mixed number 7 1 2 with a denominator of 4.]

Step: 3

= 4 1 4

[Subtract the whole numbers. Subtract the fractions.]

Correct Answer is : 4 1 4

Step: 1

Step: 2

= 43 × 3 4 × 3 - 12 × 4 3 × 4

[Rewrite the fractional part of the mixed numbers so that they have the same denominator.]

Step: 3

= 4 9 12 - 1 8 12

Step: 4

= 3 1 12

[Subtract the whole numbers and the fractions.]

Step: 5

So, 4 3 4 - 1 2 3 = 3 1 12

Correct Answer is : 3 1 12

Step: 1

Step: 2

= 62 × 2 3 × 2 - 21 × 3 2 × 3

[Rewrite the fractional part of the mixed numbers so that they have the same denominator.]

Step: 3

= 6 4 6 - 2 3 6

Step: 4

= 4 1 6

[Subtract the whole numbers and the fractions.]

Step: 5

So, 6 2 3 - 2 1 2 = 4 1 6

Correct Answer is : 4 1 6

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