Q1: What does the numerator in a fraction represent? (a) The total number of equal parts in the whole (b) How many parts are taken (c) The decimal value of the fraction (d) The reciprocal of the fraction
Solution:
Ans: (b) The numerator is the top number in a fraction that indicates how many parts are taken from the whole.
Q2: When multiplying a fraction by a whole number, what operation do we perform? (a) Multiply both numerator and denominator by the whole number (b) Multiply only the denominator by the whole number (c) Add the whole number to the numerator (d) Multiply only the numerator by the whole number
Solution:
Ans: (d) When multiplying a fraction by a whole number, we multiply the numerator with the whole number and keep the denominator same.
Q3: What is the reciprocal of 5/7? (a) 5/7 (b) 7/5 (c) 1/7 (d) 35
Solution:
Ans: (b) The reciprocal of a fraction is obtained by flipping it, so the reciprocal of 5/7 is 7/5.
Q4: When dividing a decimal number by 100, in which direction do we shift the decimal point? (a) To the right by 2 places (b) To the left by 2 places (c) To the right by 3 places (d) To the left by 1 place
Solution:
Ans: (b) When dividing by 100, we shift the decimal point to the left by 2 places as there are two zeros over one.
Q5: What is the product of two proper fractions compared to each fraction? (a) Equal to both fractions (b) Greater than both fractions (c) Smaller than both fractions (d) Sometimes greater, sometimes smaller
Solution:
Ans: (c) The value of the product of two proper fractions is smaller than each of the two fractions being multiplied.
Fill in the Blanks
Q1: A fraction consists of a numerator and a _____.
Solution:
Ans: denominator
Q2: When adding fractions with the same denominator, we add the _____ and keep the denominator the same.
Solution:
Ans: numerators
Q3: The word 'of' in fraction problems represents _____.
Solution:
Ans: multiplication
Q4: When multiplying two fractions, we multiply their numerators and _____.
Solution:
Ans: denominators
Q5: The decimal point separates the whole number part from the _____ part.
Solution:
Ans: decimal
True or False
Q1: When dividing a whole number by a fraction, we multiply that whole number by the reciprocal of that fraction.
Solution:
Ans: True This is the correct method for dividing a whole number by any fraction as stated in the content.
Q2: The product of two improper fractions is always smaller than each of the two fractions.
Solution:
Ans: False The product of two improper fractions is more than each of the two fractions, not smaller than them.
Q3: When multiplying a decimal number by 10, we shift the decimal point to the right by 1 place.
Solution:
Ans: True Multiplying by 10 shifts the decimal point right by 1 place as there is one zero over one.
Q4: To compare decimals, we first compare the decimal part before comparing the whole number part.
Solution:
Ans: False We first compare the whole number part starting from the leftmost digit before comparing the decimal parts.
Q5: When adding fractions with different denominators, we must find a common denominator first.
Solution:
Ans: True For different denominators, we find a common denominator by multiplying, then add the numerators as described.
Match the Following
Column A
Column B
1. Numerator
A. Product is 1
2. Reciprocal of a fraction
B. Tens, ones, tenths, hundredths
3. Multiplication is repeated
C. Top number of a fraction
4. Place values in decimals
D. Flip the fraction
5. Reciprocals of each other
E. Addition
Solution:
Ans:
1 - C: The numerator is the top number in a fraction indicating how many parts are taken from whole.
2 - D: The reciprocal is obtained by flipping the fraction, swapping numerator and denominator positions.
3 - E: Multiplication is repeated addition, as shown when multiplying fractions by whole numbers repeatedly.
4 - B: Decimals have place values including tens, ones, tenths, hundredths, thousandths in the place value chart.
5 - A: Non-zero numbers whose product with each other is 1 are called reciprocals of each other.
Short Answer Questions
Q1: Explain how to add two fractions with different denominators.
Solution:
Ans: To add fractions with different denominators, first find a common denominator by multiplying the denominators. Convert both fractions to equivalent fractions with this common denominator by multiplying the numerator and denominator appropriately. Then add the numerators while keeping the common denominator the same. Simplify the result if possible to get the final answer.
Q2: What happens when you multiply a decimal number by 1000? Explain with an example.
Solution:
Ans: When multiplying a decimal number by 1000, the digits remain the same but the decimal point shifts to the right by 3 places, as there are three zeros over one. For example, 0.03 × 1000 equals 30 because we shift the decimal point three places right, moving from 0.03 to 030.0, which equals 30.
Q3: How do you compare two decimal numbers? Describe the steps.
Solution:
Ans: First, compare the whole number parts of the decimals, starting from the leftmost digit. If these are equal, then compare the digits on the right of the decimal point starting from the tenths place. Continue comparing digit by digit moving right until you find different digits. The decimal with the larger digit at that position is greater.
Q4: Explain how to multiply a fraction by another fraction with an example.
Solution:
Ans: When multiplying a fraction by another fraction, multiply their numerators together and their denominators together. For example, to find 2/3 × 4/5, multiply numerators: 2 × 4 equals 8, and denominators: 3 × 5 equals 15. The product is 8/15. Simplify the result if needed to get the final answer in lowest form.
Q5: How do you divide a fraction by a whole number? Explain the method.
Solution:
Ans: When dividing a fraction by a whole number, multiply the fraction by the reciprocal of that whole number. The reciprocal of a whole number is one divided by that number. Then multiply the numerators and denominators of the fractions. For example, to divide 4/9 by 5, multiply 4/9 by 1/5 to get 4/45.
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