How many 1/8 pieces are in 1 3/8
The Correct Answer and Explanation is:
To find how many 18\frac{1}{8}81 pieces are in 1381\frac{3}{8}183, we need to express the mixed number as an improper fraction and then divide by 18\frac{1}{8}81.
Step 1: Convert 1381\frac{3}{8}183 to an improper fraction
Multiply the whole number part by the denominator and add the numerator:138=(1×8)+38=1181\frac{3}{8} = \frac{(1 \times 8) + 3}{8} = \frac{11}{8}183=8(1×8)+3=811
Step 2: Divide 118\frac{11}{8}811 by 18\frac{1}{8}81
To divide fractions, multiply by the reciprocal:118÷18=118×81=888=11\frac{11}{8} \div \frac{1}{8} = \frac{11}{8} \times \frac{8}{1} = \frac{88}{8} = 11811÷81=811×18=888=11
Final Answer:
There are 11 one-eighth pieces in 1381\frac{3}{8}183.
Explanation (about 300 words):
When dealing with fractions, especially when we want to find out how many smaller fractional parts fit into a larger amount, we use division. In this problem, we are asked to determine how many 18\frac{1}{8}81 pieces fit into 1381\frac{3}{8}183. This is a classic example of fractional division.
The first step is to convert the mixed number 1381\frac{3}{8}183 into an improper fraction. A mixed number includes both a whole number and a fraction. To convert it, multiply the whole number by the denominator of the fraction and add the numerator. So 1×8=81 \times 8 = 81×8=8, and 8+3=118 + 3 = 118+3=11. This gives us 118\frac{11}{8}811, which is an improper fraction that represents the same amount as the original mixed number.
Next, we divide 118\frac{11}{8}811 by 18\frac{1}{8}81. This is done by multiplying by the reciprocal of the divisor. The reciprocal of 18\frac{1}{8}81 is 81\frac{8}{1}18, and multiplying 118\frac{11}{8}811 by 81\frac{8}{1}18 gives 888\frac{88}{8}888, which simplifies to 11.
This means there are 11 pieces of 18\frac{1}{8}81 in 1381\frac{3}{8}183. This approach is useful in real life when slicing or measuring parts of a whole, like cutting a cake or dividing a length into smaller equal parts.
