**Problem 1 : **

Each part of a multipart question on a test is worth the same number of points. The whole question is worth 37.5 points. Daniel got 1/2 of the parts of a question correct. How many points did Daniel receive ?

**Solution : **

To find the total points received by Daniel, we have to multiply 1/2 and 37.5

We can solve this word problem using the two methods explained below.

**Method 1 : **

**Step 1 :**

Convert the decimal 3.75 as the fraction 75/2

(1/2) x 37.5 = (1/2) x (75/2)

**Step 2 :**

Multiply. Write the product in simplest form.

(1/2) x (75/2) = 75/4 = 18 3/4

So, Daniel received 18 3/4 points.

**Method 2 : **

**Step 1 :**

Convert the fraction 1/2 as the decimal 0.5

(1/2) x 37.5 = 0.5 x 37.5

**Step 2 :**

Multiply.

0.5 x 37.5 = 18.75

So, Daniel received 18.75 points.

**Problem 2 : **

The bill for a pizza was $14.50. Charles paid for 3/5 of the bill. How much did he pay ?

**Solution : **

To find the amount paid by Charles, we have to multiply 3/5 and 14.50

We can solve this word problem using the two methods explained below.

**Method 1 : **

**Step 1 :**

Convert the decimal 14.50 as the fraction 29/2

(3/5) x 14.50 = (3/5) x (29/2)

**Step 2 :**

Multiply. Write the product in simplest form.

(3/5) x (29/2) = 87/10 = 8 7/10

So, Charles paid $8 7/10.

**Method 2 : **

**Step 1 :**

Convert the fraction 3/5 as the decimal 0.6

(3/5) x 14.50 = 0.6 x 14.50

**Step 2 :**

Multiply.

0.6 x 14.50 = 8.7

So, Charles paid $8.7

**Problem 3 :**

The inner radius of a pipe is 12.625 mm and the outer radius is 18.025 mm. Find the thickness of the pipe.

**Solution :**

Thickness of the pipe is

= Outer radius - Inner radius

= 18.025 - 12.625

= 5.40 mm

**Problem 4 :**

Jennifer bought 6.5 kg of sugar. she used 3750 grams. How many kilograms of sugar were left ?

**Solution :**

3750 grams = 3750/1000 kg

3750 grams = 3.75 grams

Amount of sugar left (in kilograms) is

= 6.5 - 3.75

2.75 kg

**Problem 5 :**

Of the students in the band, 1/4 play the flute and another 1/10 play the clarinet. What fraction of the students in the band play either the flute or the clarinet ?

**Solution :**

Fraction of the students in the band play either the flute or the clarinet is

= 1/4 + 1/10

LCM of (4, 10) is 20.

So, make each denominator as 20 by multiplying the numerator and denominator of the first fraction by 5 and the second fraction by 2.

Then we have,

= (1 ⋅ 5) / (4 ⋅ 5) + (1 ⋅ 2) / (10 ⋅ 2)

= 5/20 + 2/20

= (5 + 2) / 20

= 7 / 20

So, the fraction of the students who play either the flute or the clarinet is 7/20.

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