Solve: 2/4 × 2/3 × 2/4 Using the Substitutive Property

Question

Solve the exercise using the substitutive property:

24×23×24= \frac{2}{4}\times\frac{2}{3}\times\frac{2}{4}=

Video Solution

Solution Steps

00:00 Solve using the distributive law
00:03 Use the distributive law and arrange the exercise in a way that's convenient to solve
00:11 Make sure to multiply numerator with numerator and denominator with denominator
00:18 Calculate the multiplications
00:30 Reduce the fraction as much as possible
00:35 Make sure to divide both numerator and denominator
00:41 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we need to multiply the three given fractions:
24×23×24 \frac{2}{4} \times \frac{2}{3} \times \frac{2}{4}

The steps involved in multiplying these fractions are as follows:

  • Step 1: Multiply the numerators. The numerators are 2, 2, and 2. Multiplying these together gives:
    2×2×2=82 \times 2 \times 2 = 8.
  • Step 2: Multiply the denominators. The denominators are 4, 3, and 4. Multiplying these together gives:
    4×3×4=484 \times 3 \times 4 = 48.
  • Step 3: Combine the results to form a new fraction:
    848\frac{8}{48}.
  • Step 4: Simplify the fraction. To simplify 848\frac{8}{48}, we find the greatest common divisor (GCD) of 8 and 48, which is 8. Divide both the numerator and denominator by 8:
    8÷848÷8=16\frac{8 \div 8}{48 \div 8} = \frac{1}{6}.

Therefore, the solution to the given exercise is 16\frac{1}{6}.

Answer

16 \frac{1}{6}