Addition of Fractions

Test 1Test 2
(1) ¼
¼
—		(2) 3⁄14
1⁄14
—		(1) 1⁄3
1⁄6
—		(2) 2⁄7
3⁄14
—
Test 3Test 4
(1) 3⁄5
11⁄15
—		(2) 5⁄6
1⁄2
—		(1) 1⁄7
9⁄10
—		(2) 7⁄9
1⁄4
—
Test 5Test 6
(1) 1⁄10
1⁄6
—		(2) 4⁄9
5⁄12
—		(1) 1⁄6
9⁄10
—		(2) 5⁄6
3⁄8
—

An Addition Ladder [Thorndike, '17, III, 5]

Begin at the bottom of the ladder. See if you can climb to the top without making a mistake. Be sure to copy the numbers correctly.

Step 6.a. Add 11⁄3 yd., 7⁄8 yd., 1¼ yd., 3⁄4 yd., 7⁄8 yd., and 1½ yd.
b. Add 62½¢, 662⁄3¢, 56¼¢, 60¢, and 62½¢.
c. Add 15⁄16, 19⁄32, 13⁄8, 111⁄32, and 17⁄16.
d. Add 11⁄3 yd., 1¼ yd., 1½ yd., 2 yd., 3⁄4 yd., and 2⁄3 yd.
Step 5.a. Add 4 ft. 6½ in., 53¼ in., 5 ft. ½ in., 56¾ in., and 5 ft.
b. Add 7 lb., 6 lb. 11 oz., 7½ lb., 6 lb. 4½ oz., and 8½ lb.
c. Add 1 hr. 6 min. 20 sec., 58 min. 15 sec., 1 hr. 4 min., and 55 min.
d. Add 7 dollars, 13 half dollars, 21 quarters, 17 dimes, and 19 nickels.
Step 4.a. Add .05½, .06, .04¾, .02¾, and .05¼.
b. Add .331⁄3, .12½, .18, .162⁄3, .081⁄3 and .15.
c. Add .081⁄3, .06¼, .21, .03¾, and .162⁄3.
d. Add .62, .64½, .662⁄3, .10¼, and .68.
Step 3.a. Add 7¼, 6½, 83⁄8, 5¾, 95⁄8 and 37⁄8.
b. Add 45⁄8, 12, 7½, 8¾, 6 and 5¼.
c. Add 9¾, 57⁄8, 41⁄8, 6½, 7, 35⁄8.
d. Add 12, 8½, 71⁄3, 5, 62⁄3, and 9½.
Step 2.a. Add 12.04, .96, 4.7, 9.625, 3.25, and 20.
b. Add .58, 6.03, .079, 4.206, 2.75, and 10.4.
c. Add 52, 29.8, 41.07, 1.913, 2.6, and 110.
d. Add 29.7, 315, 26.75, 19.004, 8.793, and 20.05.
Step 1.a. Add 103⁄5, 111⁄5, 104⁄5, 11, 112⁄5, 103⁄5, and 11.
b. Add 73⁄8, 65⁄8, 8, 91⁄8, 77⁄8, 53⁄8, and 81⁄8.
c. Add 21½, 18¾, 31½, 19¼, 17¼, 22, and 16½.
d. Add 145⁄12, 127⁄12, 911⁄12, 61⁄12, and 5.

A Subtraction Ladder [Thorndike, '17, III, 11]

Step 9.
a. 2.16 mi. − 1¾ mi.
c. 2 min. 10½ sec. − 93.4 sec.
e. 10 gal. 2½ qt. − 4.623 gal.		b. 5.72 ft. − 5 ft. 3 in.
d. 30.28 A. − 101⁄5 A.
Step 8.abcde
257⁄12
123⁄4
———		101⁄4
71⁄3
———		95⁄16
63⁄8
———		57⁄16
23⁄4
———		42⁄3
13⁄4
———
Step 7.abcde
283⁄4
161⁄8
———		401⁄2
143⁄8
———		101⁄4
61⁄2
———		241⁄3
111⁄2
———		371⁄2
143⁄4
———
Step 6.abcde
101⁄3
42⁄3
———		71⁄4
23⁄4
———		151⁄8
63⁄8
———		121⁄5
114⁄5
———		41⁄16
27⁄16
———
Step 5.abcde
584⁄5
521⁄5
———		662⁄3
331⁄3
———		287⁄8
75⁄8
———		62½
37½
——		97⁄12
45⁄12
——
Step 4.
a. 4 hr. − 2 hr. 17 min.
c. 1 lb. 5 oz. − 13 oz.
e. 1 bu. − 1 pk.		b. 4 lb. 7 oz. − 2 lb. 11 oz.
d. 7 ft. − 2 ft. 8 in.
Step 3.abcde
92 mi.
84.15 mi.
————		6735 mi.
6689 mi.
————		$3 − 89¢
————		28.4 mi.
18.04 mi.
————		$508.40
208.62
————
Step 2.abcde
$25.00
9.36
———		$100.00
71.28
———		$750.00
736.50
———		6124 sq. mi.
2494 sq. mi.
—————		7846 sq. mi.
2789 sq. mi.
—————
Step 1.abcde
$18.64
7.40
———		$25.39
13.37
———		$56.70
45.60
———		819.4 mi.
209.2 mi.
————		67.55 mi.
36.14 mi.
————

An Average Ladder [Thorndike, '17, III, 132]

Find the average of the quantities on each line. Begin with Step 1. Climb to the top without making a mistake. Be sure to copy the numbers correctly. Extend the division to two decimal places if necessary.

Step 6.a. 22⁄3, 17⁄8, 2¾, 4¼, 35⁄8, 3½
b. 62½¢, 662⁄3¢, 40¢, 831⁄3¢, $1.75, $2.25
c. 311⁄16, 39⁄32, 33⁄8, 317⁄32, 37⁄16
d. .17, 19, .162⁄3, .15½, .23¼, .18
Step 5.a. 5 ft. 3½ in., 61¼ in., 58¾ in., 4 ft. 11 in.
b. 6 lb. 9 oz., 6 lb. 11 oz., 7¼ lb., 73⁄8 lb.
c. 1 hr. 4 min. 40 sec., 58 min. 35 sec., 1¼ hr.
d. 2.8 miles, 3½ miles, 2.72 miles
Step 4.a. .03½, .06, .04¾, .05½, .05¼
b. .043, .045, .049, .047, .046, .045
c. 2.20, .87½, 1.18, .93¾, 1.2925, .80
d. .14½, .12½, .331⁄3, .162⁄3, .15, .17
Step 3.a. 5¼, 4½, 83⁄8, 7¾, 65⁄8, 93⁄8
b. 95⁄8, 12, 8½, 8¾, 6, 5¼, 9
c. 93⁄8, 5¾, 41⁄8, 7½, 6
d. 11, 9½, 101⁄3, 13, 162⁄3, 9½
Step 2.a. 13.05, .97, 4.8, 10.625, 3.37
b. 1.48, 7.02, .93, 5.307, 4.1, 7, 10.4
c. 68, 71.4, 59.8, 112, 96.1, 79.8
d. 2.079, 3.908, 4.165, 2.74
Step 1.a. 4, 9½, 6, 5, 7½, 8, 10, 9
b. 6, 5, 3.9, 7.1, 8
c. 1086, 1141, 1059, 1302, 1284
d. $100.82, $206.49, $317.25, $244.73