PARCC Fractions and Square Roots Practice Questions 2 — Questions and Answers

Question 1: What is 3/4 + 5/6?

8/10
8/12
19/12
1 7/12 (Correct answer)

Correct answer: 1 7/12

LCD of 4 and 6 is 12. 3/4 = 9/12; 5/6 = 10/12. Sum: 19/12 = 1 7/12.

To add fractions with unlike denominators, you must first find the least common denominator (LCD). Step 1: Find the LCD of 4 and 6. Multiples of 4: 4, 8, 12, 16... Multiples of 6: 6, 12, 18... LCD = 12 Step 2: Convert each fraction to an equivalent fraction with denominator 12. 3/4 = 3×3 / 4×3 = 9/12 5/6 = 5×2 / 6×2 = 10/12 Step 3: Add the fractions. 9/12 + 10/12 = 19/12 Step 4: Convert to a mixed number. 19/12 = 1 remainder 7 = 1 7/12 Verification: 1 7/12 is between 1 and 2, which makes sense since 3/4 ≈ 0.75 and 5/6 ≈ 0.83, and their sum ≈ 1.58 = 1 7/12 ✓ Adding fractions with unlike denominators is a foundational skill for all subsequent fraction work, including algebraic fractions. The key insight is that you can only add fractions when they have the same denominator.

Question 2: Simplify: √144

11
12 (Correct answer)
13
14

Correct answer: 12

√144 = 12 because 12 × 12 = 144.

The square root of a number is the value that, when multiplied by itself, gives the original number. In other words, if √n = x, then x² = n. For √144: we need to find a number x such that x × x = 144. 12 × 12 = 144 ✓ Therefore, √144 = 12. Knowing perfect squares helps solve square root problems quickly. Common perfect squares to memorize: 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, 7² = 49, 8² = 64, 9² = 81, 10² = 100, 11² = 121, 12² = 144, 13² = 169, 14² = 196, 15² = 225 Square roots of perfect squares are rational numbers (they can be expressed as integers or fractions). Square roots of non-perfect squares are irrational numbers (they are non-terminating, non-repeating decimals). The PARCC exam tests recognition of perfect squares and their square roots.

Question 3: What is 2/3 × 9/10?

11/30
3/5 (Correct answer)
18/13
11/13

Correct answer: 3/5

Multiply numerators and denominators: (2×9)/(3×10) = 18/30. Simplify: 18/30 = 3/5.

Multiplying fractions is straightforward: multiply the numerators together and the denominators together, then simplify the result. Step 1: Multiply numerators: 2 × 9 = 18 Step 2: Multiply denominators: 3 × 10 = 30 Result: 18/30 Step 3: Simplify by finding the GCF of 18 and 30. Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 GCF = 6 18 ÷ 6 = 3; 30 ÷ 6 = 5 Simplified: 3/5 An alternative approach is to cross-simplify before multiplying: 2/3 × 9/10: the 3 in the denominator and the 9 in the numerator share a factor of 3 (9÷3=3); the 2 in the numerator and the 10 in the denominator share a factor of 2 (10÷2=5). This gives: 1/1 × 3/5 = 3/5 ✓ Cross-simplification reduces numbers before multiplying, making computation easier. Both methods give the same result.

Question 4: Between which two consecutive integers does √50 lie?

6 and 7
7 and 8 (Correct answer)
8 and 9
5 and 6

Correct answer: 7 and 8

7² = 49 and 8² = 64. Since 49 < 50 < 64, we have 7 < √50 < 8.

To locate a square root between consecutive integers, identify the perfect squares that the number falls between. Consider the perfect squares near 50: 6² = 36 7² = 49 8² = 64 9² = 81 Since 49 < 50 < 64, taking square roots of all three values: √49 < √50 < √64 7 < √50 < 8 Therefore, √50 lies between 7 and 8. Since 50 is much closer to 49 than to 64, √50 is closer to 7 than to 8. (The actual value is approximately 7.07.) This skill—locating irrational square roots on a number line—is tested on the PARCC exam and is foundational for understanding irrational numbers. The ability to estimate square roots without a calculator requires knowledge of perfect squares and reasoning about number relationships.

Question 5: What is 5/8 ÷ 1/4?

5/32
5/2
2 1/2 (Correct answer)
1 1/4

Correct answer: 2 1/2

Dividing by a fraction means multiplying by its reciprocal: 5/8 × 4/1 = 20/8 = 5/2 = 2 1/2.

Dividing fractions follows the 'Keep, Change, Flip' (KCF) rule: 1. Keep the first fraction the same. 2. Change the division sign to multiplication. 3. Flip the second fraction (use its reciprocal). 5/8 ÷ 1/4 = 5/8 × 4/1 (flip 1/4 to get 4/1) = (5×4)/(8×1) = 20/8 Simplify 20/8: GCF of 20 and 8 is 4. 20÷4 = 5; 8÷4 = 2 = 5/2 = 2 1/2 Interpretation: 5/8 ÷ 1/4 asks 'how many 1/4s fit into 5/8?' Since 1/4 = 2/8, fitting 2/8 into 5/8 gives 2.5 times, confirming that 2 1/2 is correct. The KCF method works because dividing by a number is equivalent to multiplying by its multiplicative inverse (reciprocal). This is one of the most important fraction rules, appearing throughout mathematics from arithmetic to algebra.

Question 6: Which of the following is an irrational number?

√16
√25
√36
√20 (Correct answer)

Correct answer: √20

√16 = 4, √25 = 5, and √36 = 6 are all rational (perfect squares). √20 is irrational because 20 is not a perfect square.

A rational number can be expressed as the ratio of two integers (a fraction p/q where q ≠ 0). An irrational number cannot be expressed this way—its decimal expansion is non-terminating and non-repeating. Square roots of perfect squares are rational: √16 = 4 (rational, since 4 = 4/1) √25 = 5 (rational) √36 = 6 (rational) Square roots of non-perfect squares are irrational: √20 = √(4×5) = 2√5 ≈ 4.472135... This decimal never terminates or repeats, so √20 is irrational. The set of irrational numbers includes non-perfect square roots, the number π (pi), Euler's number e, and many others. Together, rational and irrational numbers form the set of real numbers. To quickly determine if √n is rational, check whether n is a perfect square (1, 4, 9, 16, 25, 36, 49, 64, 81, 100...). If it is, the square root is rational. If not, it is irrational. This is a fundamental concept in number theory tested on the PARCC exam.

PARCC Fractions and Square Roots Practice Questions 2

What is 3/4 + 5/6?