WHAT NUMBER MUST REPLACE X AND Y FOT THE THREE FRACTIONS TO BECOME EQUIVALENT? 16 FORTHS AND ? SEVENTHS = 44 ?
To solve this problem, we can set up an equation.
First, let's convert 16/4 to a fraction with a denominator of 7, which will give us 16/4 = (16/4) * (7/7) = 112/28.
Now we can set up the equation: 112/28 + x/7 = 44/7.
To simplify, we can multiply through by the common denominator of 28: 112 + 4x = 44.
Now, we can solve for x by subtracting 112 from both sides and then dividing by 4: 4x = -68 → x = -17.
Therefore, the number that must replace x is -17.
To find y, we can substitute the value of x back into the equation: 112/28 + (-17)/7 = 44/7.
To simplify, we can multiply through by the common denominator of 28: 112 + (-68) = 44.
This simplifies to 44 = 44, which is true.
Therefore, any number can replace y, as long as the fractions remain equivalent.
To find the missing numbers that will make the fractions equivalent, we need to compare the numerators and denominators of the fractions.
Comparing the numerators:
16/4th = 16
44/? = 44
Comparing the denominators:
4th = 4
?/7th = ?
To make the fractions equivalent, we need to have the same numerator and the same denominator.
From the numerators, we see that 16 = 44, so the missing number for x is 44.
From the denominators, we see that 4 = 7, so the missing number for y is 7.
Therefore, the missing numbers to make the fractions equivalent are x = 44 and y = 7.