Question

guided practice
which number can be moved
to change the ≠ to =?
5 + 6 + 8 ≠ 3 + 6
50¢ = __ nickels
4 feet = __ inches

Explanation:

Step1: Calculate left side sum

$5+6+8=19$

Step2: Calculate right side sum

$3+6=9$

Step3: Find difference of sums

$19-9=10$

Step4: Identify movable number

We need to move a number so both sides equal. Moving 8 from left to right: Left becomes $5+6=11$, Right becomes $3+6+8=17$ (no). Wait, move 5: Left $6+8=14$, Right $5+3+6=14$. Or move 8? No, wait: Original left=19, right=9. If we move 5 from left to right: Left $6+8=14$, Right $3+6+5=14$. Or move 8? No, wait another way: $5+6+8 = 19$, $3+6=9$. To make equal, we can move 5 to the right: $6+8 = 3+6+5$ → $14=14$. Or move 8? No, $5+6=3+6+8$ → $11≠17$. Wait, also, move 3 to left? No, question says move a number to change ≠ to =. Wait, correct: Move 5 from left to right, or move 8? No, wait, wait: $5+6+8 = 19$, $3+6=9$. The difference is 10, so moving 5 (half of 10) makes both sides 14. Alternatively, move 8? No. Wait, another option: $5+8+6$ and $3+6$. If we move 6 from left to right? No, left $5+8=13$, right $3+6+6=15$. No. The correct number is 5: moving 5 from left to right gives $6+8=3+6+5$ → $14=14$. Or moving 8? No. Wait, wait, also: $5+6+8 = 3+6+10$, no. Wait, no, let's check again. Wait, if we move 8 to the right: $5+6=3+6+8$ → $11=17$, no. If we move 3 to the left: $5+6+8+3=6$ → 22=6, no. If we move 6 from left to right: $5+8=3+6+6$ →13=15, no. Oh! Wait, I made a mistake. What if we move 5 to the right? No, wait, $5+6+8 = 19$, $3+6=9$. If we move 8 from left to right? No. Wait, wait, maybe move 5 to the right, but no, 19-5=14, 9+5=14. Yes, that works. Or is there another number? Wait, no, the other way: move 3 to the left? 19+3=22, 9-3=6, no. So the number is 5.

Step5: Solve nickel conversion

1 nickel = 5¢, so $\frac{50}{5}=10$

Step6: Solve feet to inches

1 foot = 12 inches, so $4\times12=48$

Answer:

1. The number 5 (moving it from the left side to the right side makes $6+8=3+6+5$, which simplifies to $14=14$)
2. 10
3. 48